Simulace.info - User contributions [en]

WS 2022/2023

2023-01-27T10:05:29Z

Luxa00: /* Simulations */

Semestral papers from winter term 2022/2023. Please, put here links to the pages with your paper. First you need to have your [[Assignments WS 2022/2023|assignment approved]]

==Simulations==
--[[User:Luxa00|Luxa00]] ([[User talk:Luxa00|talk]]) 11:03, 27 January 2023(CET) Divorce prediction for 50 years: [[Divorce prediction for 50 years]]

--[[User:Julian Bleyer|Julian Bleyer]] ([[User talk:Xkrep33|talk]]) 0:44, 18 January 2023(CET) Aircraft Evacuation Simulation: [[Airplane_Evacuation]]

--[[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 13:55, 18 January 2023 (CET) Cartel simulation with leniency program by Rebecca Baumann (baur00): [[cartel_simulation]]

--[[User:Kock06|Kock06]] ([[User talk:Kock06|talk]]) 14:03, 22 January(GTM+8) Receivables prediction by Monte Carlo simulation: [[Receivables]]

--[[User:Ruzv01|Ruzv01]] ([[User talk:Ruzv01|talk]]) 10:33, 22 January(CET) Household electricity consumption: [[Household electricity consumption]]

--[[User:Haki00|Haki00]] ([[User talk:Haki00|talk]]) 21:38, 22 January(CET) Artsakh blockade: [[Artsakh blockade]]

--[[User:Edema|Edema]] ([[User talk:Haki00|talk]]) 22:00, 22 January(CET) Mortgage Assessment: [[Mortgage Assessment]]

--[[User:BortnikSvitlana|BortnikSvitlana]] ([[User talk:BortnikSvitlana|talk]]) 22:36, 22 January(CET) Traffic Simulation at an Intersection: [[Traffic Simulation at an Intersection]]

--[[User:Ceta|Ceta]] ([[User talk:Ceta|talk]]) 22:48, 22 January 2023 (CET) Pumped hydroelectric energy storage (PHES)System Simulation [[Pump_storage]]

--[[User:Botd00|Botd00]] ([[User talk:Botd00|talk]]) 22:46, 22 January(CET) Twitter Simulation: [[Twitter simulation]]

-- [[User:Miln02|Miln02]] ([[User talk:Miln02|talk]]) 23:05, 22 January 2023 (CET) Saving for an apartment [[Savingforanapartment]]

-- [[User:Abizah1|Abizah1]] ([[User talk:Abizah1|talk]]) 23:55, 22 January 2023 (CET) https://www.simulace.info/index.php/Boxing_athlete

-- [[User:Pierreatekwana1|Pierreatekwana1]] ([[User talk:Pierreatekwana1|talk]]) 00:24, 23 January 2023 (CET) Crop yield simulation: [[Cropyield]]

-- [[User:Kane02|Kane02]] ([[User talk:Kane02|talk]]) 18:52, 23 January 2023 (CET) Car Park Solution for a New Cinema [[Car Park Solution for a New Cinema]]

-- [[User:Kadt02|Kadt02]] ([[User talk:Kadt02|talk]]) 19:43, 23 January 2023 (CET) Comparing searching stategies [[Finding strategies comparison]]

-- [[User:Ploo00|Ploo00]] ([[User talk:Ploo00|talk]]) 19:50, 25 January 2023 (CET) Profit in store vs e-shop [[Profit in store vs e-shop]]

-- [[User:Prin03vse|Prin03vse]] ([[User talk:Prin03vse|talk]]) 23:35, 25 January 2023 (CET) NBA Game Simulation [[NBA game simulation]]

File:Divorce.zip

2023-01-27T09:59:39Z

Luxa00:

Divorce prediction for 50 years

2023-01-27T09:59:12Z

Luxa00: /* Code */

Divorce prediction for 50 years

2023-01-27T09:53:32Z

Luxa00: /* Macro factors */

Divorce prediction for 50 years

2023-01-27T09:53:06Z

Luxa00: /* Parameters calculation */

File:Luxa00model.PNG

2023-01-27T09:52:48Z

Luxa00:

Divorce prediction for 50 years

2023-01-27T09:52:17Z

Luxa00: /* Macro factors */

File:Luxa00loop.PNG

2023-01-27T09:51:45Z

Luxa00:

File:Luxa005.png

2023-01-27T09:51:02Z

Luxa00:

File:Luxa004.png

2023-01-27T09:50:49Z

Luxa00:

Divorce prediction for 50 years

2023-01-27T09:50:27Z

Luxa00: /* Results */

File:Contested divorce.png

2023-01-27T09:48:22Z

Luxa00:

File:Luxa002.png

2023-01-27T09:47:11Z

Luxa00: Macro factors

== Summary ==
Macro factors

Divorce prediction for 50 years

2023-01-27T09:46:43Z

Luxa00: /* Parameters calculation */

Divorce prediction for 50 years

2023-01-27T09:44:45Z

Luxa00: /* Macro factors */

Divorce prediction for 50 years

2023-01-27T09:44:16Z

Luxa00: /* Results */

File:Luxa001.png

2023-01-27T09:43:37Z

Luxa00:

Divorce prediction for 50 years

2023-01-26T21:14:58Z

Luxa00:

Divorce prediction for 50 years

2023-01-26T21:13:20Z

Luxa00:

Divorce prediction for 50 years

2023-01-26T21:11:57Z

Luxa00: /* Macro factors */

=Problem definition=
Divorce is unfortunately very common in the current time. The reasons are various, all of them are however stated in the divorce papers. To be able to get divorced, the ex-couple must always attend at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the number of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

=Method=
Because there were multiple independent risk factors and reasons that cause divorce identified, Vensim was evaluated as the best tool for the performance of the simulation. The simulation uses data from the Czech Statistical Office and also studies on the reasons for divorce; all the data is from year 2009 to 2021 as older data could not be found and 12 years’ worth of data has been evaluated to be sufficient. ''Note: Please note that the data for 2022 will be published in October 2023, therefore data up to the year 2021 is be used for this simulation.
''
=Detailed description of the method=
https://www.simulace.info/index.php?title=Divorce_prediction_for_50_years&action=edit
=Problem definition=
Divorce is unfortunately very common in the current time. The reasons are various, all of them are however stated in the divorce papers. To be able to get divorced, the ex-couple must always attend at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the number of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

=Method=
Because there were multiple independent risk factors and reasons that cause divorce identified, Vensim was evaluated as the best tool for the performance of the simulation. The simulation uses data from the Czech Statistical Office and also studies on the reasons for divorce; all the data is from year 2009 to 2021 as older data could not be found and 12 years’ worth of data has been evaluated to be sufficient. ''Note: Please note that the data for 2022 will be published in October 2023, therefore data up to the year 2021 is be used for this simulation.
''
=Detailed description of the method=
== Micro causes of the divorce ==
The document ''Statistická ročenka České republiky'', which is published every year in October by the Czech Statistical Office, contains chapter ''C.10 Rozvody podle příčiny rozvratu manželství (Divorces: by cause of marriage breakdown)'' with the reasons for divorce, as stated by the divorcees in the divorce papers. The reasons are as follows:
a/ Ill-considered marriage
b/ Alcoholism
c/ Infidelity
d/ Lack of interest in the family (incl. abandon. of living together)
e/ Ill-treatment, criminal conviction
f/ Different characters, views and interests
g/ Health reasons
h/ Sexual discord
i/ Other causes
j/ Cause not given

After an examination of the data, two unclear reason categories were identified – “Other causes” and “Cause not given”. Based on further research, it was discovered that in case in the year 2014, a new amendment to the Divorce Act has been introduced and put into effect. Based on this, the divorces were categorized as (a) uncontested or (b) contested. The first of the categories describes the situation, where both partners agree on all requirements of the divorce, for example the division of properties and caring for the offspring, in such case, the court does not try to discover the reason for the separation, therefore these cases are the ones in the “Cause not given” category. On the other hand, during the resolution of the contested divorce, the court does search for the reason of the breakup of the marriage. The enforcement of the amendment in 2014 is clearly visible in the data, where the “Cause not given” reason rises extremely since the affected year. (Jirsa, 2014) The second reason category “Other causes” describes the cases, which cannot be classified as any of the other reasons available and is used during the solution of the contested divorce.

Additionally, it is important to point out that the reasons for the divorce are stated by both parties (wife, husband), meaning that there were twice as much reasons as there were divorces. To be able to process this discrepancy, the sums of reasons as stated by the women were added to the relevant sums of reasons stated by the men and this value was divided by 2 to ensure that there was a same amount on data on causes as there were divorces. Because of this method, it is possible to see values with decimal point in the data set – this is not a mistake though. Example (we abstract from other reasons): 22 women said that the reason for the ending of their marriage was infidelity. On the other hand, 18 men also stated the same reason for their divorce, the data from the Czech Statistical Office would show 20 divorces for this case, however if we add up the reasons, we would get a total of 40 divorces as both parties are obligated to state their reason. For the sake of this simulation, the total number of the listed causes would be added up and divided by two, resulting in the number of 20 infidelity caused divorces.

Additionally, it is important to point out that the reasons for the divorce are stated by both parties (wife, husband), meaning that there were twice as much reasons as there were divorces. To be able to process this discrepancy, the sums of reasons as stated by the women were added to the relevant sums of reasons stated by the men and this value was divided by 2 to ensure that there was a same amount on data on causes as there were divorces. Because of this method, it is possible to see values with decimal point in the data set – this is not a mistake though.

''Example (we abstract from other reasons): 22 women said that the reason for the ending of their marriage was infidelity. On the other hand, 18 men also stated the same reason for their divorce, the data from the Czech Statistical Office would show 20 divorces for this case, however if we add up the reasons, we would get a total of 40 divorces as both parties are obligated to state their reason. For the sake of this simulation, the total number of the listed causes would be added up and divided by two, resulting in the number of 20 infidelity caused divorces.''

== Macro factors ==
For the prediction of the future divorce, the factors identified in the studies by Scott, S. B. et al. (2013) and Hawkins et al. (2012), Fučík (2013) and IDFA (not dated) were used. The factors are:
* '''Religion (Hawkins et al., 2012)''' – the more religious people there are, the less divorces.
* '''Level of education (Fučík, 2013)''' – the higher level of education (high school and above) means less divorces – parameter is named People with higher education.
* '''Women’s financial independence''' (Society, 2018) – the more financially independent women are, the more divorce there will be.
* '''Money issues (IDFA, not dated)''' – the more money issues there are, the more divorce. Parameter is named Country economic performance.

Firstly, the amount of religious Czech citizens was analysed using the data from the relevant Census of the Czech Republic, i.e., data from 2011 and 2021 census. It was found that the amount of Czech religious people is lowering. This information is not in line with the result of the study and therefore this parameter cannot be used. Next, using the same data, let us talk about the Education level parameter. The theory states that the there are people with higher education, the less likely they are to get a divorce, the data for the divorce shows the that this trend is true for the analysed data set. Thirdly, the data from Czech Statistical office was used again, this time it was the ''A3 Podíly zaměstnanců, placený čas a hrubé měsíční mzdy podle věku a pohlaví'' part of the ''Struktura mezd zaměstnanců'' publication, which describes the salary information of Czech citizens. Data for all the analysed years was found and it was identified that the ratio of Men’s Average salary to Women’s Average salary was rising in the time, reaching the highest number of 88 %, average salary paid to women is continuously getting closer to men. This proves that over the analysed years, women are getting paid more and therefore becoming more financially independent. Unfortunately, this parameter also cannot be used for the calculation of divorces as no significand trend was identified.

Next, by studying the data of people born in specific years from ''Statistická ročenka České republiky'', the effect of the amount of people in the risk age (defined as 40 to 49) to the number of divorces was identified. It was tested using the Czech statistical office data about the amount of people born in each year. In 8 out of 12 cases, the number of people in the risk age was rising in comparison to the prior year. Thus, it was evaluated that the trend denies the theory that the population age affects the number of people involved in the divorce and this parameter cannot therefore be used for the simulation.

Let us now test the theory about money issues causing divorce. Economic situation in the families is mostly affected by the country economic situation. Using the data about the Czech Gross domestic product from the ''VYBRANÉ UKAZATELE NÁRODNÍHO HOSPODÁŘSTVÍ'' chapter of the ''Statistická ročenka České republiky'' published by the Czech Statistical office data. It was proven that as the Czech Gross domestic product grew, the number of divorces lowered. This parameter can therefore be used in the simulation.

After testing the influence of all the factors on the divorce amount, two of the factors were disqualified as the relevant data were found to not prove the theory stated in the quoted studies. Two factors have however been discovered to show the same trend as the divorce in the Czech Republic during the observed years, these factors can therefore be used in the following way:

A/ '''Level of education''' – parameter will be named '''Increase of people with higher education''' (secondary and tertiary education), it will be calculated as the increase since the prior year:
<code> = Number of people with higher educationT1 / Number of people with higher educationT0 </code>
The impact of this factor on the yearly divorce has proven to be inverse proportion, the more people with high school and above, mean less divorces.

B/ '''Money issues''' – parameter will be named '''Increase in the gross domestic product''', it will be calculated in the same way as described above, and its impact on the divorce has proven to be inverse proportion = the higher the gross domestic product, the more divorces.

These two factors can explain the lowering numbers of total yearly divorces in the analysed data and in this simulation, their average will be used to predict the Macro factors. Together with the '''Randomness factor divorce''', which will describe the difference between expected in the predicted value and the reality, the number of divorces will be simulated. The parameters for the randomness factor will be derived from the mistakes in the past predictions. Using the values from the past and the normal distribution, the Randomness factor will be calculated for each year.

Additionally, the parameter ''Number of new marriages'' was added as well as the ''Number of active marriages'', calculated from the data from the Czech Statistical Office. These were added because of the logical rule – the more marriages there are, the more divorces there would be.

In the research of the factors of the number of new marriages, the study by Pew research Centre (Pew Research Centre 2010) was found. It states that there is a positive correlation between the amount of higher-educated people (secondary and tertiary education) and the number of marriages. Secondly, the study also says that the better the economical situation, the more new marriages there will be. Same as in the previous cases, these theories have also been tested, this time, it was against the data about new marriages, stated in the (at this point well-known) publication ''Statistická ročenka České republiky''. Both theories were confirmed, setting two new rules – the higher the gross product, the more new marriages and the higher the number of university educated people, the more new marriages. Lastly, it is logical that the number of adults in the country also affects the number of new marriages, therefore this factor will also be used and it will be generated from the historical data about the number of adults as counted by the Czech Statistical Office. The parameter '''Randomness factor marriage''' will be calculated similarly to the Randomness factor divorce and used the same way. It is interesting to note that the prediction based on the average change in the two observed factors was very accurate, except for the covid-affected years. Since life is full of such unpredictable events, the covid years will not be taken out of the calculations.

<code> New marriagesT1 = Marriage RateT0 * Macro FactorsT0 * Number Of AdultsT0 + Randomness Factor Marriage </code>

After all the theories were verified, the Causal Loop Diagram using only the parameters that were confirmed in the previous part, all using the identified theories and data from the Czech Statistical Office.

[[File:luxa00loop]]

On the basis of the Causal Loop Diagram and using all the calculated data from 2009 to 2021, the Stock and Flow Diagram was created.

==Parameters calculation==
Although the parameters have already been introduced, let us explain the calculations that will be used for the simulation. The auxiliary calculations can be found in the Data file. As mentioned, the years used for the calculations were 2009 to 2021 (except for the education calculation, which used years 2015 to 2021).

Firstly, there are the '''Micro causes of the divorce'''. All the causes will be simulated separately as the random normal. The parameters for this formula were calculated based on the obtained historical data. The Subcategory Contested divorce is calculated as the sum of the numbers of causes within the category and the total number of Micro causes of the divorce is calculated as the sum of the two subcategories.

<code> Contested divorce = Alcoholism + Different characters, views and interests + Ill considered marriage + Ill treatment, criminal conviction + Infidelity + Lack of interest in the family + Other causes + Sexual discord + Health reasons </code>

<code> Micro causes of the divorce = Uncontested divorce + Contested divorce </code>

'''Macro factors''' describe the average of increase in the number of people with higher education and increase in the gross domestic product. Both increases were counted as the random normal, again based on the yearly historical data. Average of these two parameters was calculated as their sum divided by two.

The meaning and the mathematical base of the '''Randomness factor for divorce''' and '''for marriage''' was described in the previous chapter. In the simulation, it was calculated based on the random normal.

'''Number of adults''' was calculated as the random normal from the historical number of Czech citizens aged 18 and more. It is interesting to note that this number has been almost constant in the last 12 years.

'''Marriage rate''' explains the ratio of new marriages to the total amount of adults = New marriages / Number of adults. In the simulation, this was counted randomly based on the historical calculations of the marriage rate. Disclaimer: this counts the number of married couples, not the number of married individuals.

Finally, let us introduce the main parameters.
'''Number of divorces''' is a calculation of the effect of the Macro factors on the number of divorces (calculated within the micro causes of divorce) with addition of the '''Randomness factor divorce'''.

<code> Number of divorces = (Macro factors) * Micro causes of the divorce + Randomness factor divorce </code>

The '''Number of marriages''' is calculated similarly. It calculates the effects of the marriage rate and macro factors on the number of new marriages.

<code> Number of marriages = Marriage rate * Macro factors * Number of adults + Randomness factor marriage </code>

'''Number of active marriages''' is the number of currently married couples. This parameter has a set initial value, which is the number of married couples in 2021: 2006844,5 (the reason for the number with a decimal value is described in the chapter Micro causes of the divorce). The parameter will further be increased by the number of new marriages and decreased by the number of divorces.

<code> Number of active marriages = Number of new marriages - Number of divorces </code>

=Results=
The simulation shows the number of the active marriages is rising in time, with the maximum of 3.05 million marriages at the end of the simulation, i.e., 50 years from 2021. The number of new marriages is relatively stable, between 45000 and 60000. The number of divorces is a little less stable than the number of new marriages, the value is between 25000 and 41000.

[[File:luxa001.jpg]]

[[File:luxa002.jpg]]

[[File:luxa003.jpg]]

[[File:luxa004.jpg]]

[[File:luxa005.jpg]]

=Conclusion=

The results disprove the claim that people used to be more committed in the “good old days. However, the simulation does not show a significant lowering in the number of divorces – the maximum number of the divorces shown in the simulation is 45000, which is 15000 more than the maximum detected in the data in analysed years 2009-2021. Based on this and looking at the problems defined at the beginning of this paper, the court capacity and the number of divorce lawyers should slightly rise in the 50-year future.

=Code=

=Sources=
The data sources are placed within the data.xlsx file.

FUČÍK, Petr, 2013. Rozvod a změny reprodukčních strategií. Brno: Masarykova univerzit. ISBN 978-80-210-6093-7.

HAWKINS et al., 2012. Reasons for Divorce and Openness to Marital Reconciliation. Journal of Divorce & Remarriage. 53. 453-463. 10.1080/10502556.2012.682898.

IDFA, not dated. Why People Divorce and What are the Reasons for Divorce?. Find a Certified Divorce Financial Analyst (CDFA) Professionals [online]. Dostupné z: https://institutedfa.com/Leading-Causes-Divorce/

JIRSA, Jaromír, 2014. Nová úprava rozvodového řízení účinná od 1. 1. 2014 | Právní prostor. Právní prostor | Informační web nejen pro právníky [online]. Copyright © 1999 [cit. 22.01.2023]. Dostupné z: https://www.pravniprostor.cz/clanky/obcanske-pravo/nova-uprava-rozvodoveho-rizeni-ucinna-od-1-1-2014

PEW RESEARCH CENTRE, 2010. THE DECLINE OF MARRIAGE AND RISE OF NEW FAMILIES. Pew Research Center’s Social & Demographic Trends Project. Online. 18 November 2010. [Accessed 25 January 2023]. Retrieved from: https://www.pewresearch.org/social-trends/2010/11/18/the-decline-of-marriage-and-rise-of-new-families/

== Macro factors ==
For the prediction of the future divorce, the factors identified in the studies by Scott, S. B. et al. (2013) and Hawkins et al. (2012), Fučík (2013) and IDFA (not dated) were used. The factors are:
* '''Religion (Hawkins et al., 2012)''' – the more religious people there are, the less divorces.
* '''Level of education (Fučík, 2013)''' – the higher level of education (high school and above) means less divorces – parameter is named People with higher education.
* '''Women’s financial independence''' (Society, 2018) – the more financially independent women are, the more divorce there will be.
* '''Money issues (IDFA, not dated)''' – the more money issues there are, the more divorce. Parameter is named Country economic performance.

Firstly, the amount of religious Czech citizens was analysed using the data from the relevant Census of the Czech Republic, i.e., data from 2011 and 2021 census. It was found that the amount of Czech religious people is lowering. This information is not in line with the result of the study and therefore this parameter cannot be used. Next, using the same data, let us talk about the Education level parameter. The theory states that the there are people with higher education, the less likely they are to get a divorce, the data for the divorce shows the that this trend is true for the analysed data set. Thirdly, the data from Czech Statistical office was used again, this time it was the ''A3 Podíly zaměstnanců, placený čas a hrubé měsíční mzdy podle věku a pohlaví'' part of the ''Struktura mezd zaměstnanců'' publication, which describes the salary information of Czech citizens. Data for all the analysed years was found and it was identified that the ratio of Men’s Average salary to Women’s Average salary was rising in the time, reaching the highest number of 88 %, average salary paid to women is continuously getting closer to men. This proves that over the analysed years, women are getting paid more and therefore becoming more financially independent. Unfortunately, this parameter also cannot be used for the calculation of divorces as no significand trend was identified.
Next, by studying the data of people born in specific years from ''Statistická ročenka České republiky'', the effect of the amount of people in the risk age (defined as 40 to 49) to the number of divorces was identified. It was tested using the Czech statistical office data about the amount of people born in each year. In 8 out of 12 cases, the number of people in the risk age was rising in comparison to the prior year. Thus, it was evaluated that the trend denies the theory that the population age affects the number of people involved in the divorce and this parameter cannot therefore be used for the simulation.
Let us now test the theory about money issues causing divorce. Economic situation in the families is mostly affected by the country economic situation. Using the data about the Czech Gross domestic product from the ''VYBRANÉ UKAZATELE NÁRODNÍHO HOSPODÁŘSTVÍ'' chapter of the ''Statistická ročenka České republiky'' published by the Czech Statistical office data. It was proven that as the Czech Gross domestic product grew, the number of divorces lowered. This parameter can therefore be used in the simulation.

After testing the influence of all the factors on the divorce amount, two of the factors were disqualified as the relevant data were found to not prove the theory stated in the quoted studies. Two factors have however been discovered to show the same trend as the divorce in the Czech Republic during the observed years, these factors can therefore be used in the following way:
A/ '''Level of education''' – parameter will be named '''Increase of people with higher education''' (secondary and tertiary education), it will be calculated as the increase since the prior year:
<code> = Number of people with higher educationT1 / Number of people with higher educationT0 <pre>
The impact of this factor on the yearly divorce has proven to be inverse proportion, the more people with high school and above, mean less divorces.

B/ '''Money issues''' – parameter will be named '''Increase in the gross domestic product''', it will be calculated in the same way as described above, and its impact on the divorce has proven to be inverse proportion = the higher the gross domestic product, the more divorces.
These two factors can explain the lowering numbers of total yearly divorces in the analysed data and in this simulation, their average will be used to predict the Macro factors. Together with the '''Randomness factor divorce''', which will describe the difference between expected in the predicted value and the reality, the number of divorces will be simulated. The parameters for the randomness factor will be derived from the mistakes in the past predictions. Using the values from the past and the normal distribution, the Randomness factor will be calculated for each year.
Additionally, the parameter ''Number of new marriages'' was added as well as the ''Number of active marriages'', calculated from the data from the Czech Statistical Office. These were added because of the logical rule – the more marriages there are, the more divorces there would be.

In the research of the factors of the number of new marriages, the study by Pew research Centre (Pew Research Centre 2010) was found. It states that there is a positive correlation between the amount of higher-educated people (secondary and tertiary education) and the number of marriages. Secondly, the study also says that the better the economical situation, the more new marriages there will be. Same as in the previous cases, these theories have also been tested, this time, it was against the data about new marriages, stated in the (at this point well-known) publication ''Statistická ročenka České republiky''. Both theories were confirmed, setting two new rules – the higher the gross product, the more new marriages and the higher the number of university educated people, the more new marriages. Lastly, it is logical that the number of adults in the country also affects the number of new marriages, therefore this factor will also be used and it will be generated from the historical data about the number of adults as counted by the Czech Statistical Office. The parameter '''Randomness factor marriage''' will be calculated similarly to the Randomness factor divorce and used the same way. It is interesting to note that the prediction based on the average change in the two observed factors was very accurate, except for the covid-affected years. Since life is full of such unpredictable events, the covid years will not be taken out of the calculations.

<code> New marriagesT1 = Marriage RateT0 * Macro FactorsT0 * Number Of AdultsT0 + Randomness Factor Marriage </code>

After all the theories were verified, the Causal Loop Diagram using only the parameters that were confirmed in the previous part, all using the identified theories and data from the Czech Statistical Office.
On the basis of the Causal Loop Diagram and using all the calculated data from 2009 to 2021, the Stock and Flow Diagram was created.

==Parameters calculation==
Although the parameters have already been introduced, let us explain the calculations that will be used for the simulation. The auxiliary calculations can be found in the Data file. As mentioned, the years used for the calculations were 2009 to 2021 (except for the education calculation, which used years 2015 to 2021).

Firstly, there are the '''Micro causes of the divorce'''. All the causes will be simulated separately as the random normal. The parameters for this formula were calculated based on the obtained historical data. The Subcategory Contested divorce is calculated as the sum of the numbers of causes within the category and the total number of Micro causes of the divorce is calculated as the sum of the two subcategories.

<code> Contested divorce = Alcoholism + Different characters, views and interests + Ill considered marriage + Ill treatment, criminal conviction + Infidelity + Lack of interest in the family + Other causes + Sexual discord + Health reasons </code>

<code> Micro causes of the divorce = Uncontested divorce + Contested divorce </code>

'''Macro factors''' describe the average of increase in the number of people with higher education and increase in the gross domestic product. Both increases were counted as the random normal, again based on the yearly historical data. Average of these two parameters was calculated as their sum divided by two.

The meaning and the mathematical base of the '''Randomness factor for divorce''' and '''for marriage''' was described in the previous chapter. In the simulation, it was calculated based on the random normal.

'''Number of adults''' was calculated as the random normal from the historical number of Czech citizens aged 18 and more. It is interesting to note that this number has been almost constant in the last 12 years.

'''Marriage rate''' explains the ratio of new marriages to the total amount of adults = New marriages / Number of adults. In the simulation, this was counted randomly based on the historical calculations of the marriage rate. Disclaimer: this counts the number of married couples, not the number of married individuals.

Finally, let us introduce the main parameters.
'''Number of divorces''' is a calculation of the effect of the Macro factors on the number of divorces (calculated within the micro causes of divorce) with addition of the '''Randomness factor divorce'''.

<code> Number of divorces = (Macro factors) * Micro causes of the divorce + Randomness factor divorce </code>

The '''Number of marriages''' is calculated similarly. It calculates the effects of the marriage rate and macro factors on the number of new marriages.

<code> Number of marriages = Marriage rate * Macro factors * Number of adults + Randomness factor marriage </code>

'''Number of active marriages''' is the number of currently married couples. This parameter has a set initial value, which is the number of married couples in 2021: 2006844,5 (the reason for the number with a decimal value is described in the chapter Micro causes of the divorce). The parameter will further be increased by the number of new marriages and decreased by the number of divorces.

<code> Number of active marriages = Number of new marriages - Number of divorces </code>

=Results=
The simulation shows the number of the active marriages is rising in time, with the maximum of 3.05 million marriages at the end of the simulation, i.e., 50 years from 2021. The number of new marriages is relatively stable, between 45000 and 60000. The number of divorces is a little less stable than the number of new marriages, the value is between 25000 and 41000.
[[File:Example.jpg]]

=Conclusion=

=Code=

Divorce prediction for 50 years

2023-01-26T21:10:54Z

Luxa00:

=Problem definition=
Divorce is unfortunately very common in the current time. The reasons are various, all of them are however stated in the divorce papers. To be able to get divorced, the ex-couple must always attend at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the number of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

=Method=
Because there were multiple independent risk factors and reasons that cause divorce identified, Vensim was evaluated as the best tool for the performance of the simulation. The simulation uses data from the Czech Statistical Office and also studies on the reasons for divorce; all the data is from year 2009 to 2021 as older data could not be found and 12 years’ worth of data has been evaluated to be sufficient. ''Note: Please note that the data for 2022 will be published in October 2023, therefore data up to the year 2021 is be used for this simulation.
''
=Detailed description of the method=
https://www.simulace.info/index.php?title=Divorce_prediction_for_50_years&action=edit
=Problem definition=
Divorce is unfortunately very common in the current time. The reasons are various, all of them are however stated in the divorce papers. To be able to get divorced, the ex-couple must always attend at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the number of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

=Method=
Because there were multiple independent risk factors and reasons that cause divorce identified, Vensim was evaluated as the best tool for the performance of the simulation. The simulation uses data from the Czech Statistical Office and also studies on the reasons for divorce; all the data is from year 2009 to 2021 as older data could not be found and 12 years’ worth of data has been evaluated to be sufficient. ''Note: Please note that the data for 2022 will be published in October 2023, therefore data up to the year 2021 is be used for this simulation.
''
=Detailed description of the method=
== Micro causes of the divorce ==
The document ''Statistická ročenka České republiky'', which is published every year in October by the Czech Statistical Office, contains chapter ''C.10 Rozvody podle příčiny rozvratu manželství (Divorces: by cause of marriage breakdown)'' with the reasons for divorce, as stated by the divorcees in the divorce papers. The reasons are as follows:
a/ Ill-considered marriage
b/ Alcoholism
c/ Infidelity
d/ Lack of interest in the family (incl. abandon. of living together)
e/ Ill-treatment, criminal conviction
f/ Different characters, views and interests
g/ Health reasons
h/ Sexual discord
i/ Other causes
j/ Cause not given

After an examination of the data, two unclear reason categories were identified – “Other causes” and “Cause not given”. Based on further research, it was discovered that in case in the year 2014, a new amendment to the Divorce Act has been introduced and put into effect. Based on this, the divorces were categorized as (a) uncontested or (b) contested. The first of the categories describes the situation, where both partners agree on all requirements of the divorce, for example the division of properties and caring for the offspring, in such case, the court does not try to discover the reason for the separation, therefore these cases are the ones in the “Cause not given” category. On the other hand, during the resolution of the contested divorce, the court does search for the reason of the breakup of the marriage. The enforcement of the amendment in 2014 is clearly visible in the data, where the “Cause not given” reason rises extremely since the affected year. (Jirsa, 2014) The second reason category “Other causes” describes the cases, which cannot be classified as any of the other reasons available and is used during the solution of the contested divorce.

Additionally, it is important to point out that the reasons for the divorce are stated by both parties (wife, husband), meaning that there were twice as much reasons as there were divorces. To be able to process this discrepancy, the sums of reasons as stated by the women were added to the relevant sums of reasons stated by the men and this value was divided by 2 to ensure that there was a same amount on data on causes as there were divorces. Because of this method, it is possible to see values with decimal point in the data set – this is not a mistake though. Example (we abstract from other reasons): 22 women said that the reason for the ending of their marriage was infidelity. On the other hand, 18 men also stated the same reason for their divorce, the data from the Czech Statistical Office would show 20 divorces for this case, however if we add up the reasons, we would get a total of 40 divorces as both parties are obligated to state their reason. For the sake of this simulation, the total number of the listed causes would be added up and divided by two, resulting in the number of 20 infidelity caused divorces.

Additionally, it is important to point out that the reasons for the divorce are stated by both parties (wife, husband), meaning that there were twice as much reasons as there were divorces. To be able to process this discrepancy, the sums of reasons as stated by the women were added to the relevant sums of reasons stated by the men and this value was divided by 2 to ensure that there was a same amount on data on causes as there were divorces. Because of this method, it is possible to see values with decimal point in the data set – this is not a mistake though.

''Example (we abstract from other reasons): 22 women said that the reason for the ending of their marriage was infidelity. On the other hand, 18 men also stated the same reason for their divorce, the data from the Czech Statistical Office would show 20 divorces for this case, however if we add up the reasons, we would get a total of 40 divorces as both parties are obligated to state their reason. For the sake of this simulation, the total number of the listed causes would be added up and divided by two, resulting in the number of 20 infidelity caused divorces.''

== Macro factors ==
For the prediction of the future divorce, the factors identified in the studies by Scott, S. B. et al. (2013) and Hawkins et al. (2012), Fučík (2013) and IDFA (not dated) were used. The factors are:
* '''Religion (Hawkins et al., 2012)''' – the more religious people there are, the less divorces.
* '''Level of education (Fučík, 2013)''' – the higher level of education (high school and above) means less divorces – parameter is named People with higher education.
* '''Women’s financial independence''' (Society, 2018) – the more financially independent women are, the more divorce there will be.
* '''Money issues (IDFA, not dated)''' – the more money issues there are, the more divorce. Parameter is named Country economic performance.

Firstly, the amount of religious Czech citizens was analysed using the data from the relevant Census of the Czech Republic, i.e., data from 2011 and 2021 census. It was found that the amount of Czech religious people is lowering. This information is not in line with the result of the study and therefore this parameter cannot be used. Next, using the same data, let us talk about the Education level parameter. The theory states that the there are people with higher education, the less likely they are to get a divorce, the data for the divorce shows the that this trend is true for the analysed data set. Thirdly, the data from Czech Statistical office was used again, this time it was the ''A3 Podíly zaměstnanců, placený čas a hrubé měsíční mzdy podle věku a pohlaví'' part of the ''Struktura mezd zaměstnanců'' publication, which describes the salary information of Czech citizens. Data for all the analysed years was found and it was identified that the ratio of Men’s Average salary to Women’s Average salary was rising in the time, reaching the highest number of 88 %, average salary paid to women is continuously getting closer to men. This proves that over the analysed years, women are getting paid more and therefore becoming more financially independent. Unfortunately, this parameter also cannot be used for the calculation of divorces as no significand trend was identified.

Next, by studying the data of people born in specific years from ''Statistická ročenka České republiky'', the effect of the amount of people in the risk age (defined as 40 to 49) to the number of divorces was identified. It was tested using the Czech statistical office data about the amount of people born in each year. In 8 out of 12 cases, the number of people in the risk age was rising in comparison to the prior year. Thus, it was evaluated that the trend denies the theory that the population age affects the number of people involved in the divorce and this parameter cannot therefore be used for the simulation.

Let us now test the theory about money issues causing divorce. Economic situation in the families is mostly affected by the country economic situation. Using the data about the Czech Gross domestic product from the ''VYBRANÉ UKAZATELE NÁRODNÍHO HOSPODÁŘSTVÍ'' chapter of the ''Statistická ročenka České republiky'' published by the Czech Statistical office data. It was proven that as the Czech Gross domestic product grew, the number of divorces lowered. This parameter can therefore be used in the simulation.

After testing the influence of all the factors on the divorce amount, two of the factors were disqualified as the relevant data were found to not prove the theory stated in the quoted studies. Two factors have however been discovered to show the same trend as the divorce in the Czech Republic during the observed years, these factors can therefore be used in the following way:

A/ '''Level of education''' – parameter will be named '''Increase of people with higher education''' (secondary and tertiary education), it will be calculated as the increase since the prior year:
<code> = Number of people with higher educationT1 / Number of people with higher educationT0 </code>
The impact of this factor on the yearly divorce has proven to be inverse proportion, the more people with high school and above, mean less divorces.

B/ '''Money issues''' – parameter will be named '''Increase in the gross domestic product''', it will be calculated in the same way as described above, and its impact on the divorce has proven to be inverse proportion = the higher the gross domestic product, the more divorces.

These two factors can explain the lowering numbers of total yearly divorces in the analysed data and in this simulation, their average will be used to predict the Macro factors. Together with the '''Randomness factor divorce''', which will describe the difference between expected in the predicted value and the reality, the number of divorces will be simulated. The parameters for the randomness factor will be derived from the mistakes in the past predictions. Using the values from the past and the normal distribution, the Randomness factor will be calculated for each year.

Additionally, the parameter ''Number of new marriages'' was added as well as the ''Number of active marriages'', calculated from the data from the Czech Statistical Office. These were added because of the logical rule – the more marriages there are, the more divorces there would be.

In the research of the factors of the number of new marriages, the study by Pew research Centre (Pew Research Centre 2010) was found. It states that there is a positive correlation between the amount of higher-educated people (secondary and tertiary education) and the number of marriages. Secondly, the study also says that the better the economical situation, the more new marriages there will be. Same as in the previous cases, these theories have also been tested, this time, it was against the data about new marriages, stated in the (at this point well-known) publication ''Statistická ročenka České republiky''. Both theories were confirmed, setting two new rules – the higher the gross product, the more new marriages and the higher the number of university educated people, the more new marriages. Lastly, it is logical that the number of adults in the country also affects the number of new marriages, therefore this factor will also be used and it will be generated from the historical data about the number of adults as counted by the Czech Statistical Office. The parameter '''Randomness factor marriage''' will be calculated similarly to the Randomness factor divorce and used the same way. It is interesting to note that the prediction based on the average change in the two observed factors was very accurate, except for the covid-affected years. Since life is full of such unpredictable events, the covid years will not be taken out of the calculations.

<code> New marriagesT1 = Marriage RateT0 * Macro FactorsT0 * Number Of AdultsT0 + Randomness Factor Marriage </code>

After all the theories were verified, the Causal Loop Diagram using only the parameters that were confirmed in the previous part, all using the identified theories and data from the Czech Statistical Office.
On the basis of the Causal Loop Diagram and using all the calculated data from 2009 to 2021, the Stock and Flow Diagram was created.

==Parameters calculation==
Although the parameters have already been introduced, let us explain the calculations that will be used for the simulation. The auxiliary calculations can be found in the Data file. As mentioned, the years used for the calculations were 2009 to 2021 (except for the education calculation, which used years 2015 to 2021).

Firstly, there are the '''Micro causes of the divorce'''. All the causes will be simulated separately as the random normal. The parameters for this formula were calculated based on the obtained historical data. The Subcategory Contested divorce is calculated as the sum of the numbers of causes within the category and the total number of Micro causes of the divorce is calculated as the sum of the two subcategories.

<code> Contested divorce = Alcoholism + Different characters, views and interests + Ill considered marriage + Ill treatment, criminal conviction + Infidelity + Lack of interest in the family + Other causes + Sexual discord + Health reasons </code>

<code> Micro causes of the divorce = Uncontested divorce + Contested divorce </code>

'''Macro factors''' describe the average of increase in the number of people with higher education and increase in the gross domestic product. Both increases were counted as the random normal, again based on the yearly historical data. Average of these two parameters was calculated as their sum divided by two.

The meaning and the mathematical base of the '''Randomness factor for divorce''' and '''for marriage''' was described in the previous chapter. In the simulation, it was calculated based on the random normal.

'''Number of adults''' was calculated as the random normal from the historical number of Czech citizens aged 18 and more. It is interesting to note that this number has been almost constant in the last 12 years.

'''Marriage rate''' explains the ratio of new marriages to the total amount of adults = New marriages / Number of adults. In the simulation, this was counted randomly based on the historical calculations of the marriage rate. Disclaimer: this counts the number of married couples, not the number of married individuals.

Finally, let us introduce the main parameters.
'''Number of divorces''' is a calculation of the effect of the Macro factors on the number of divorces (calculated within the micro causes of divorce) with addition of the '''Randomness factor divorce'''.

<code> Number of divorces = (Macro factors) * Micro causes of the divorce + Randomness factor divorce </code>

The '''Number of marriages''' is calculated similarly. It calculates the effects of the marriage rate and macro factors on the number of new marriages.

<code> Number of marriages = Marriage rate * Macro factors * Number of adults + Randomness factor marriage </code>

'''Number of active marriages''' is the number of currently married couples. This parameter has a set initial value, which is the number of married couples in 2021: 2006844,5 (the reason for the number with a decimal value is described in the chapter Micro causes of the divorce). The parameter will further be increased by the number of new marriages and decreased by the number of divorces.

<code> Number of active marriages = Number of new marriages - Number of divorces </code>

=Results=
The simulation shows the number of the active marriages is rising in time, with the maximum of 3.05 million marriages at the end of the simulation, i.e., 50 years from 2021. The number of new marriages is relatively stable, between 45000 and 60000. The number of divorces is a little less stable than the number of new marriages, the value is between 25000 and 41000.

[[File:luxa001.jpg]]

[[File:luxa002.jpg]]

[[File:luxa003.jpg]]

[[File:luxa004.jpg]]

[[File:luxa005.jpg]]

=Conclusion=

The results disprove the claim that people used to be more committed in the “good old days. However, the simulation does not show a significant lowering in the number of divorces – the maximum number of the divorces shown in the simulation is 45000, which is 15000 more than the maximum detected in the data in analysed years 2009-2021. Based on this and looking at the problems defined at the beginning of this paper, the court capacity and the number of divorce lawyers should slightly rise in the 50-year future.

=Code=

=Sources=
The data sources are placed within the data.xlsx file.

FUČÍK, Petr, 2013. Rozvod a změny reprodukčních strategií. Brno: Masarykova univerzit. ISBN 978-80-210-6093-7.

HAWKINS et al., 2012. Reasons for Divorce and Openness to Marital Reconciliation. Journal of Divorce & Remarriage. 53. 453-463. 10.1080/10502556.2012.682898.

IDFA, not dated. Why People Divorce and What are the Reasons for Divorce?. Find a Certified Divorce Financial Analyst (CDFA) Professionals [online]. Dostupné z: https://institutedfa.com/Leading-Causes-Divorce/

JIRSA, Jaromír, 2014. Nová úprava rozvodového řízení účinná od 1. 1. 2014 | Právní prostor. Právní prostor | Informační web nejen pro právníky [online]. Copyright © 1999 [cit. 22.01.2023]. Dostupné z: https://www.pravniprostor.cz/clanky/obcanske-pravo/nova-uprava-rozvodoveho-rizeni-ucinna-od-1-1-2014

PEW RESEARCH CENTRE, 2010. THE DECLINE OF MARRIAGE AND RISE OF NEW FAMILIES. Pew Research Center’s Social & Demographic Trends Project. Online. 18 November 2010. [Accessed 25 January 2023]. Retrieved from: https://www.pewresearch.org/social-trends/2010/11/18/the-decline-of-marriage-and-rise-of-new-families/

== Macro factors ==
For the prediction of the future divorce, the factors identified in the studies by Scott, S. B. et al. (2013) and Hawkins et al. (2012), Fučík (2013) and IDFA (not dated) were used. The factors are:
* '''Religion (Hawkins et al., 2012)''' – the more religious people there are, the less divorces.
* '''Level of education (Fučík, 2013)''' – the higher level of education (high school and above) means less divorces – parameter is named People with higher education.
* '''Women’s financial independence''' (Society, 2018) – the more financially independent women are, the more divorce there will be.
* '''Money issues (IDFA, not dated)''' – the more money issues there are, the more divorce. Parameter is named Country economic performance.

Firstly, the amount of religious Czech citizens was analysed using the data from the relevant Census of the Czech Republic, i.e., data from 2011 and 2021 census. It was found that the amount of Czech religious people is lowering. This information is not in line with the result of the study and therefore this parameter cannot be used. Next, using the same data, let us talk about the Education level parameter. The theory states that the there are people with higher education, the less likely they are to get a divorce, the data for the divorce shows the that this trend is true for the analysed data set. Thirdly, the data from Czech Statistical office was used again, this time it was the ''A3 Podíly zaměstnanců, placený čas a hrubé měsíční mzdy podle věku a pohlaví'' part of the ''Struktura mezd zaměstnanců'' publication, which describes the salary information of Czech citizens. Data for all the analysed years was found and it was identified that the ratio of Men’s Average salary to Women’s Average salary was rising in the time, reaching the highest number of 88 %, average salary paid to women is continuously getting closer to men. This proves that over the analysed years, women are getting paid more and therefore becoming more financially independent. Unfortunately, this parameter also cannot be used for the calculation of divorces as no significand trend was identified.
Next, by studying the data of people born in specific years from ''Statistická ročenka České republiky'', the effect of the amount of people in the risk age (defined as 40 to 49) to the number of divorces was identified. It was tested using the Czech statistical office data about the amount of people born in each year. In 8 out of 12 cases, the number of people in the risk age was rising in comparison to the prior year. Thus, it was evaluated that the trend denies the theory that the population age affects the number of people involved in the divorce and this parameter cannot therefore be used for the simulation.
Let us now test the theory about money issues causing divorce. Economic situation in the families is mostly affected by the country economic situation. Using the data about the Czech Gross domestic product from the ''VYBRANÉ UKAZATELE NÁRODNÍHO HOSPODÁŘSTVÍ'' chapter of the ''Statistická ročenka České republiky'' published by the Czech Statistical office data. It was proven that as the Czech Gross domestic product grew, the number of divorces lowered. This parameter can therefore be used in the simulation.

After testing the influence of all the factors on the divorce amount, two of the factors were disqualified as the relevant data were found to not prove the theory stated in the quoted studies. Two factors have however been discovered to show the same trend as the divorce in the Czech Republic during the observed years, these factors can therefore be used in the following way:
A/ '''Level of education''' – parameter will be named '''Increase of people with higher education''' (secondary and tertiary education), it will be calculated as the increase since the prior year:
<code> = Number of people with higher educationT1 / Number of people with higher educationT0 <pre>
The impact of this factor on the yearly divorce has proven to be inverse proportion, the more people with high school and above, mean less divorces.

B/ '''Money issues''' – parameter will be named '''Increase in the gross domestic product''', it will be calculated in the same way as described above, and its impact on the divorce has proven to be inverse proportion = the higher the gross domestic product, the more divorces.
These two factors can explain the lowering numbers of total yearly divorces in the analysed data and in this simulation, their average will be used to predict the Macro factors. Together with the '''Randomness factor divorce''', which will describe the difference between expected in the predicted value and the reality, the number of divorces will be simulated. The parameters for the randomness factor will be derived from the mistakes in the past predictions. Using the values from the past and the normal distribution, the Randomness factor will be calculated for each year.
Additionally, the parameter ''Number of new marriages'' was added as well as the ''Number of active marriages'', calculated from the data from the Czech Statistical Office. These were added because of the logical rule – the more marriages there are, the more divorces there would be.

In the research of the factors of the number of new marriages, the study by Pew research Centre (Pew Research Centre 2010) was found. It states that there is a positive correlation between the amount of higher-educated people (secondary and tertiary education) and the number of marriages. Secondly, the study also says that the better the economical situation, the more new marriages there will be. Same as in the previous cases, these theories have also been tested, this time, it was against the data about new marriages, stated in the (at this point well-known) publication ''Statistická ročenka České republiky''. Both theories were confirmed, setting two new rules – the higher the gross product, the more new marriages and the higher the number of university educated people, the more new marriages. Lastly, it is logical that the number of adults in the country also affects the number of new marriages, therefore this factor will also be used and it will be generated from the historical data about the number of adults as counted by the Czech Statistical Office. The parameter '''Randomness factor marriage''' will be calculated similarly to the Randomness factor divorce and used the same way. It is interesting to note that the prediction based on the average change in the two observed factors was very accurate, except for the covid-affected years. Since life is full of such unpredictable events, the covid years will not be taken out of the calculations.

<code> New marriagesT1 = Marriage RateT0 * Macro FactorsT0 * Number Of AdultsT0 + Randomness Factor Marriage </code>

After all the theories were verified, the Causal Loop Diagram using only the parameters that were confirmed in the previous part, all using the identified theories and data from the Czech Statistical Office.
On the basis of the Causal Loop Diagram and using all the calculated data from 2009 to 2021, the Stock and Flow Diagram was created.

==Parameters calculation==
Although the parameters have already been introduced, let us explain the calculations that will be used for the simulation. The auxiliary calculations can be found in the Data file. As mentioned, the years used for the calculations were 2009 to 2021 (except for the education calculation, which used years 2015 to 2021).

Firstly, there are the '''Micro causes of the divorce'''. All the causes will be simulated separately as the random normal. The parameters for this formula were calculated based on the obtained historical data. The Subcategory Contested divorce is calculated as the sum of the numbers of causes within the category and the total number of Micro causes of the divorce is calculated as the sum of the two subcategories.

<code> Contested divorce = Alcoholism + Different characters, views and interests + Ill considered marriage + Ill treatment, criminal conviction + Infidelity + Lack of interest in the family + Other causes + Sexual discord + Health reasons </code>

<code> Micro causes of the divorce = Uncontested divorce + Contested divorce </code>

'''Macro factors''' describe the average of increase in the number of people with higher education and increase in the gross domestic product. Both increases were counted as the random normal, again based on the yearly historical data. Average of these two parameters was calculated as their sum divided by two.

The meaning and the mathematical base of the '''Randomness factor for divorce''' and '''for marriage''' was described in the previous chapter. In the simulation, it was calculated based on the random normal.

'''Number of adults''' was calculated as the random normal from the historical number of Czech citizens aged 18 and more. It is interesting to note that this number has been almost constant in the last 12 years.

'''Marriage rate''' explains the ratio of new marriages to the total amount of adults = New marriages / Number of adults. In the simulation, this was counted randomly based on the historical calculations of the marriage rate. Disclaimer: this counts the number of married couples, not the number of married individuals.

Finally, let us introduce the main parameters.
'''Number of divorces''' is a calculation of the effect of the Macro factors on the number of divorces (calculated within the micro causes of divorce) with addition of the '''Randomness factor divorce'''.

<code> Number of divorces = (Macro factors) * Micro causes of the divorce + Randomness factor divorce </code>

The '''Number of marriages''' is calculated similarly. It calculates the effects of the marriage rate and macro factors on the number of new marriages.

<code> Number of marriages = Marriage rate * Macro factors * Number of adults + Randomness factor marriage </code>

'''Number of active marriages''' is the number of currently married couples. This parameter has a set initial value, which is the number of married couples in 2021: 2006844,5 (the reason for the number with a decimal value is described in the chapter Micro causes of the divorce). The parameter will further be increased by the number of new marriages and decreased by the number of divorces.

<code> Number of active marriages = Number of new marriages - Number of divorces </code>

=Results=
The simulation shows the number of the active marriages is rising in time, with the maximum of 3.05 million marriages at the end of the simulation, i.e., 50 years from 2021. The number of new marriages is relatively stable, between 45000 and 60000. The number of divorces is a little less stable than the number of new marriages, the value is between 25000 and 41000.
[[File:Example.jpg]]

=Conclusion=

=Code=

Divorce prediction for 50 years

2023-01-26T20:59:35Z

Luxa00: Created page with "=Problem definition= Divorce is unfortunately very common in the current time. The reasons are various, all of them are however stated in the divorce papers. To be able to get..."

Assignments WS 2022/2023

2022-12-15T22:21:38Z

Luxa00: /* The prediction of divorce rate in Czech Republic for the following 50 years */

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== Effect of leniency programs on cartel rates by [[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 11:18, 7 December 2022 (CET) ==

''' Simulation '''

The leniency program of the European Commission offers the companies involved in a cartel either complete or partial immunity from fines if they self-report and hand over evidence. It was introduced in 1996, following the surge in amnesty applications in the wake of the 1993 revision of the Corporate Leniency Program of the US Department of Justice’s Antitrust Division. Reports from various implemented leniency programs showed that such programs led to numerous applications. However, despite the clear increase in leniency applications, the question poses itself as to whether the programs were also successful in a sense that the actual cartel rate in those countries declined.
The simulation will be based on a study of Harrington and Chang from 2015, in which they concluded the following:

• The actual cartel rate decreases in case that the leniency program does not affect the non-leniency enforcement

• But: if the non-leniency enforcement is affected because resources are shifted to the prosecution of leniency application cases, there might be two possibilities, the cartel rate might increase.

This simulation focuses on the latter case. Assuming endogenized non-leniency enforcement, the introduction of a leniency program might have a differential impact on different industries. If a leniency program is introduced, the cartels that are about to collapse will seek to self-report. This in turn shifts resources from exposing active cartels to prosecuting cartels that are already collapsing. This creates more work for the authorities, who, instead of focusing on active cartels may now focus on dying cartels. This crowding-out effect coming about with the introduction of a leniency program shall be simulated in this project.

''' Goal '''

The simulation will have the following objectives:

* Illustrate the change in cartel rates and the change in the average life expectancy of a cartel triggered by the introduction of a leniency program in case of endogenized non-leniency enforcement for industries with unstable cartels (e.g. industries with a high number of competitors, or demand with more price elasticity) and for industries with stable cartels (e.g. industries with less competitors and demand with less price elasticity).
* Illustrate how many resources may be shifted from non-leniency enforcement to prosecuting leniency application cases without it having an undesired effect on the actual cartel rate.

''' Practical relevance '''

The simulation may be used by law enforcement officials to evaluate whether a leniency program leads to the desired effect (i.e. the decrease in the cartel rate) or not. Also, it can help for deciding whether the non-leniency enforcement needs to be strengthened to prevent the crowding-out effect.

''' Method '''

The described scenario is a multi-agent simulation in which the agents are pursuing a utility-based approach. Thus, the simulation will be done with NetLogo.
The following features will be included into the simulation:

- For both industries with stable and industries with unstable cartels:

* Number of active cartels (dying after reaching avg. life expectancy)
* Number of competitors
* Average life expectancy of a cartel
* “Birth” of new cartels

- For leniency/non-leniency enforcement:
* Resources and their assignment to either leniency or non-leniency enforcement
* Capacity of taking down an active cartel
* Capacity of taking down a cartel based on leniency applications

The simulation will be based on the 2015 research from Harrington and Chang as well as on publicly accessible data from the European Commission regarding antitrust cases from 1964 until today.

''' Sources '''
* Harrington Jr, J. E., & Chang, M. H. (2015). When can we expect a corporate leniency program to result in fewer cartels?. The Journal of Law and Economics, 58(2), 417-449.
* Ordóñez‐De‐Haro, J. M., Borrell, J. R., & Jiménez, J. L. (2018). The European commission's fight against cartels (1962–2014): A retrospective and forensic analysis. JCMS: Journal of Common Market Studies, 56(5), 1087-1107.

[[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 11:18, 7 December 2022 (CET) Rebecca Baumann (baur00)

: This isn't an easy topic. Be careful about available data. '''Approved''' [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 01:46, 15 December 2022 (CET)

== The prediction of divorce rate in Czech Republic for the following 50 years ==

''' The goal of the simulation '''

Divorce in the Czech republic must always contain at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the amount of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

''' Method '''

Vensim will be used for this simulation. The used data will come from the Czech Statistical Office and possibly other sources (Refer to [1] and [2]), such as published studies on the most common reasons for divorce. When possible, the data about each reason of divorce will be also found and the simulation model will contain this data.

== Edit: additional details ==

''' What all parameters will the simulation work with and how?'''

1. Number of marriages – the more marriages, the more divorces

a/ Number of people in the age 25 to 34 (i.e., the most common age to get married) – the more there is of these people, the more marriages there will be

b/ Number of divorced people in the age 40 to 49 (i.e., the most common age to get re-married after a divorce) – the more there is of these people, the more marriages there will be, however not as much as the number above

2. Micro causes of divorces = Top 10 causes of divorce as researched by the Czech Statistical Office, published yearly – the more common are these causes (alcoholism, infidelity etc), the more divorces there will be

a/ Ill-considered marriage

b/ Alcoholism

c/ Infidelity

d/ Lack of interest in the family (incl. abandon. of living together)

e/ Ill-treatment, criminal conviction

f/ Different characters, views and interests

g/ Health reasons

h/ Sexual discord

i/ Other causes

j/ Cause not given

3. Number of people in the age 40 to 49 – the more there is of these people, the more divorces there will be (it is the most common age to get divorced)

4. Macro causes of divorces

a/ Economic independence of women = the more economically independent women are, the more likely they are to divorce in case of an unhappy marriage – this will be evaluated through a comparison of data of average income of men vs. women

b/ Being religious – divorce is far less common for religious people.

''' What data source will be used for deriving the equations?'''

Based on my current research of data sources, the Czech Statistical Office has the all the data necessary for this paper.

[1] Scott, S. B., Rhoades, G. K., Stanley, S. M., Allen, E. S., & Markman, H. J. (2013). Reasons for Divorce and Recollections of Premarital Intervention: Implications for Improving Relationship Education. Couple & family psychology, 2(2), 131–145. https://doi.org/10.1037/a0032025

[2] Hawkins, Alan & Willoughby, Brian & Doherty, William. (2012). Reasons for Divorce and Openness to Marital Reconciliation. Journal of Divorce & Remarriage. 53. 453-463. 10.1080/10502556.2012.682898.

: Sounds interesting, but I miss more detail about the simulation. What all parameters will the simulation work with and how? What data source will be used for deriving the equations? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 11:03, 15 December 2022 (CET)

==Crop Yield Forecasting==

''' Simulation '''

Crop growth and development simulations and yield forecasting will be performed using variables such as crop type, planting date, soil type, soil texture, and climate data (temperature, rainfall, etc.).

'''Problem definition'''

Arable land is increasingly limited, while the world's population has steadily been increasing over the years. In order to meet rapidly rising demand, production must be increased while natural resources must be protected. New agricultural research is needed to provide information on how to achieve sustainable agriculture in the face of global climate variability. Predicting crop yield under different conditions, such as different irrigation regimes, planting dates, and crop management practices, has become critical for farmers and other stakeholders who use these predictions to make more informed decisions about how to allocate resources, such as labor, equipment, and inputs, to maximize yield and productivity.

'''Method'''

Crop yield simulation tools include AquaCrop, DSSAT, and CropSyst. These tools use mathematical models to simulate crop growth and development based on input data like weather, soil type, and management practices. These tools use this data to estimate the crop's potential yield, as well as other important factors like water use and crop evapotranspiration. For this assignment I will be using AquaCrop which is a crop water productivity model developed by the United Nations Food and Agriculture Organization (FAO). It is used to simulate crop growth and yield under various environmental and management conditions. AquaCrop simulates crop growth and development, and estimates yield based on soil conditions, climate, irrigation, and management practices. The application gives access to various FAO databases with all the necessary data needed to perform a comprehensive simulation of the crop yield.

'''Citations'''

* Y. Lu, C. Wei, M. F. McCabe, and J. Sheffield, “Multi-variable assimilation into a modified AquaCrop model for improved maize simulation without management or crop phenology information,” Agricultural Water Management, vol. 266, p. 107576, May 2022, doi: 10.1016/j.agwat.2022.107576.
* P. N. Kephe, K. K. Ayisi, and B. M. Petja, “Challenges and opportunities in crop simulation modelling under seasonal and projected climate change scenarios for crop production in South Africa,” Agriculture & Food Security, vol. 10, no. 1, p. 10, Apr. 2021, doi: 10.1186/s40066-020-00283-5.
* N. T. Olivera, O. B. Manrique, Y. G. Masjuan, and A. M. G. Alega, “Evaluation of AquaCrop model in crop dry bean growth simulation,” Revista Ciencias Técnicas Agropecuarias, vol. 25, no. 3, pp. 23–30, Accessed: Dec. 10, 2022. [Online]. Available: https://www.redalyc.org/journal/932/93246970003/html/
* N. Pirmoradian, Z. Saadati, M. Rezaei, and M. R. Khaledian, “Simulating water productivity of paddy rice under irrigation regimes using AquaCrop model in humid and semiarid regions of Iran,” Appl Water Sci, vol. 10, no. 7, p. 161, Jun. 2020, doi: 10.1007/s13201-020-01249-5.

[[User:Pierreatekwana|Pierreatekwana]] ([[User talk:Pierreatekwana|talk]]) 15:06, 15 December 2022 (CET)

Talk:Assignments WS 2022/2023

2022-12-14T20:18:53Z

Luxa00: Divorces in Czech Republic in the following 50 years

== What will be simulated ==
The prediction of divorce rate in Czech Republic for the following 50 years.

== The goal of the simulation ==
Divorce in the Czech republic must always contain at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the amount of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

== Method ==
Vensim will be used for this simulation. The used data will come from the Czech Statistical Office and possibly other sources (Refer to [1] and [2]), such as published studies on the most common reasons for divorce. When possible, the data about each reason of divorce will be also found and the simulation model will contain this data.

[1] Scott, S. B., Rhoades, G. K., Stanley, S. M., Allen, E. S., & Markman, H. J. (2013). Reasons for Divorce and Recollections of Premarital Intervention: Implications for Improving Relationship Education. Couple & family psychology, 2(2), 131–145. https://doi.org/10.1037/a0032025

[2] Hawkins, Alan & Willoughby, Brian & Doherty, William. (2012). Reasons for Divorce and Openness to Marital Reconciliation. Journal of Divorce & Remarriage. 53. 453-463. 10.1080/10502556.2012.682898.