USL Project 3
Zuzanna Kowalczyk
Assosiation Rules on Divorce Data
Topic of intrest
In this project, I delve into the dynamics of marital relationships using association rules, analyzing a dataset of 170 responses to 55 variables. The dataset explores sentiments on shared values, communication styles, and conflict resolution in 54 questions, along with one variable indicating marital status (is the person divorced or not).
By uncovering hidden patterns and associations, I aim to gain insights into factors influencing marital success or challenges. Statements like “I feel aggressive when I argue with my wife” or “I know my wife’s hopes and wishes” prompt exploration of correlations that may reveal predictors of relationship satisfaction.
This analysis aims to contribute to a deeper understanding of marital dynamics, offering insights for fostering healthier and more fulfilling relationships.
Data preparation
Before starting to work with the dataset I’m loading all the needed libraries for further analysis.
library(dplyr)
library(arules)
library(arulesViz)
library(ggplot2)
library(gridExtra)The source of the data set is an online repository. The dataset does not have any missing values and is constructed in a way that each row has answers to each of the questions about the relationship and the column that has the information about the status of the marrige, divorced or not divorced.For simplicity all the variables are called Atr and the number of question that the attribute adheres to, each question was has encoded values of answers on a five point Likter’s scale.
The original data gathering process is described in Yöntem et al., 2019 with the divorce predictor scale itself developed in Yöntem et al., 2018 which isn’t unfortunately available in English. Each question was answered on a scale from 0 to 4 depending on how strongly the participants agreed with the statement.
Questions:
When one of our apologies apologizes when our discussions go in a bad direction, the issue does not extend.
I know we can ignore our differences, even if things get hard sometimes.
When we need it, we can take our discussions with my wife from the beginning and correct it.
When I argue with my wife, it will eventually work for me to contact him.
The time I spent with my wife is special for us.
We don’t have time at home as partners.
We are like two strangers who share the same environment at home rather than family.
I enjoy our holidays with my wife.
I enjoy traveling with my wife.
My wife and most of our goals are common.
I think that one day in the future, when I look back, I see that my wife and I are in harmony with each other.
My wife and I have similar values in terms of personal freedom.
My husband and I have similar entertainment.
Most of our goals for people (children, friends, etc.) are the same.
Our dreams of living with my wife are similar and harmonious
We’re compatible with my wife about what love should be
We share the same views with my wife about being happy in your life
My wife and I have similar ideas about how marriage should be
My wife and I have similar ideas about how roles should be in marriage
My wife and I have similar values in trust
I know exactly what my wife likes.
I know how my wife wants to be taken care of when she’s sick.
I know my wife’s favorite food.
I can tell you what kind of stress my wife is facing in her life.
I have knowledge of my wife’s inner world.
I know my wife’s basic concerns.
I know what my wife’s current sources of stress are.
I know my wife’s hopes and wishes.
I know my wife very well.
I know my wife’s friends and their social relationships.
I feel aggressive when I argue with my wife.
When discussing with my wife, I usually use expressions such as as ‘you always’ or ‘you never’.
I can use negative statements about my wife’s personality during our discussions.
I can use offensive expressions during our discussions.
I can insult our discussions.
I can be humiliating when we argue.
My argument with my wife is not calm.
I hate my wife’s way of bringing it up.
Fights often occur suddenly.
We’re just starting a fight before I know what’s going on.
When I talk to my wife about something, my calm suddenly breaks.
When I argue with my wife, it only snaps in and I don’t say a word.
I’m mostly thirsty to calm the environment a little bit.
Sometimes I think it’s good for me to leave home for a while.
I’d rather stay silent than argue with my wife.
Even if I’m right in the argument, I’m thirsty not to upset the other side.
When I argue with my wife, I remain silent because I am afraid of not being able to control my anger.
I feel right in our discussions.
I have nothing to do with what I’ve been accused of.
I’m not actually the one who’s guilty about what I’m accused of.
I’m not the one who’s wrong about problems at home.
I wouldn’t hesitate to tell her about my wife’s inadequacy.
When I discuss it, I remind her of my wife’s inadequate issues.
I’m not afraid to tell her about my wife’s incompetence.
divorce<-read.csv("divorce.csv",sep=";")
divorce <- divorce %>% rename(Divorced=Class)
print(colnames(divorce))## [1] "Atr1" "Atr2" "Atr3" "Atr4" "Atr5"
## [6] "Atr6" "Atr7" "Atr8" "Atr9" "Atr10"
## [11] "Atr11" "Atr12" "Atr13" "Atr14" "Atr15"
## [16] "Atr16" "Atr17" "Atr18" "Atr19" "Atr20"
## [21] "Atr21" "Atr22" "Atr23" "Atr24" "Atr25"
## [26] "Atr26" "Atr27" "Atr28" "Atr29" "Atr30"
## [31] "Atr31" "Atr32" "Atr33" "Atr34" "Atr35"
## [36] "Atr36" "Atr37" "Atr38" "Atr39" "Atr40"
## [41] "Atr41" "Atr42" "Atr43" "Atr44" "Atr45"
## [46] "Atr46" "Atr47" "Atr48" "Atr49" "Atr50"
## [51] "Atr51" "Atr52" "Atr53" "Atr54" "Divorced"divorce[, c(1:55)] <- lapply(divorce[, c(1:55)], factor)
print(str(divorce),
max.tbl.height = 200,
method = "render")## 'data.frame': 170 obs. of 55 variables:
## $ Atr1 : Factor w/ 5 levels "0","1","2","3",..: 3 5 3 4 3 1 4 3 3 2 ...
## $ Atr2 : Factor w/ 5 levels "0","1","2","3",..: 3 5 3 3 3 1 4 2 3 2 ...
## $ Atr3 : Factor w/ 5 levels "0","1","2","3",..: 5 5 3 4 2 2 4 3 2 2 ...
## $ Atr4 : Factor w/ 5 levels "0","1","2","3",..: 2 5 3 3 2 1 3 3 1 2 ...
## $ Atr5 : Factor w/ 5 levels "0","1","2","3",..: 1 5 2 4 2 1 2 3 1 2 ...
## $ Atr6 : Factor w/ 5 levels "0","1","2","3",..: 1 1 4 4 2 3 4 2 5 3 ...
## $ Atr7 : Factor w/ 5 levels "0","1","2","3",..: 1 1 3 4 1 1 5 1 2 1 ...
## $ Atr8 : Factor w/ 5 levels "0","1","2","3",..: 1 5 2 4 1 1 4 4 4 3 ...
## $ Atr9 : Factor w/ 5 levels "0","1","2","3",..: 1 5 2 4 1 1 3 4 4 3 ...
## $ Atr10 : Factor w/ 5 levels "0","1","2","3",..: 1 5 3 4 1 2 3 3 4 3 ...
## $ Atr11 : Factor w/ 5 levels "0","1","2","3",..: 2 5 4 5 1 1 3 5 4 4 ...
## $ Atr12 : Factor w/ 5 levels "0","1","2","3",..: 1 4 5 4 2 3 3 4 4 1 ...
## $ Atr13 : Factor w/ 5 levels "0","1","2","3",..: 2 5 3 4 1 2 3 3 4 1 ...
## $ Atr14 : Factor w/ 5 levels "0","1","2","3",..: 2 1 4 5 2 1 4 4 4 3 ...
## $ Atr15 : Factor w/ 5 levels "0","1","2","3",..: 1 5 4 4 2 3 3 5 4 2 ...
## $ Atr16 : Factor w/ 5 levels "0","1","2","3",..: 2 5 4 4 2 1 4 4 4 1 ...
## $ Atr17 : Factor w/ 5 levels "0","1","2","3",..: 1 5 4 4 2 3 4 3 4 2 ...
## $ Atr18 : Factor w/ 5 levels "0","1","2","3",..: 1 5 4 4 2 2 4 4 4 3 ...
## $ Atr19 : Factor w/ 5 levels "0","1","2","3",..: 1 4 4 4 3 1 4 3 4 2 ...
## $ Atr20 : Factor w/ 5 levels "0","1","2","3",..: 2 3 3 5 2 2 3 2 4 1 ...
## $ Atr21 : Factor w/ 5 levels "0","1","2","3",..: 1 2 2 2 2 1 4 3 3 1 ...
## $ Atr22 : Factor w/ 5 levels "0","1","2","3",..: 1 2 1 2 1 1 4 2 3 1 ...
## $ Atr23 : Factor w/ 5 levels "0","1","2","3",..: 1 1 2 2 1 1 4 2 3 1 ...
## $ Atr24 : Factor w/ 5 levels "0","1","2","3",..: 1 3 3 2 1 1 4 3 4 2 ...
## $ Atr25 : Factor w/ 5 levels "0","1","2","3",..: 1 3 3 3 1 3 3 4 3 2 ...
## $ Atr26 : Factor w/ 5 levels "0","1","2","3",..: 1 2 3 2 3 3 4 4 4 2 ...
## $ Atr27 : Factor w/ 5 levels "0","1","2","3",..: 1 3 3 2 2 1 4 3 3 2 ...
## $ Atr28 : Factor w/ 5 levels "0","1","2","3",..: 1 1 3 2 3 1 3 3 4 2 ...
## $ Atr29 : Factor w/ 5 levels "0","1","2","3",..: 1 2 4 2 2 1 3 3 3 2 ...
## $ Atr30 : Factor w/ 5 levels "0","1","2","3",..: 2 2 3 4 2 1 3 4 4 2 ...
## $ Atr31 : Factor w/ 5 levels "0","1","2","3",..: 2 1 4 3 2 5 2 2 2 2 ...
## $ Atr32 : Factor w/ 5 levels "0","1","2","3",..: 3 5 4 4 2 2 3 2 2 2 ...
## $ Atr33 : Factor w/ 5 levels "0","1","2","3",..: 2 3 2 3 2 2 3 1 2 1 ...
## $ Atr34 : Factor w/ 5 levels "0","1","2","3",..: 3 4 2 3 2 2 2 3 2 2 ...
## $ Atr35 : Factor w/ 5 levels "0","1","2","3",..: 1 1 2 2 1 2 2 3 2 1 ...
## $ Atr36 : Factor w/ 5 levels "0","1","2","3",..: 2 3 2 2 1 2 3 2 2 1 ...
## $ Atr37 : Factor w/ 5 levels "0","1","2","3",..: 3 4 3 4 1 2 4 5 2 2 ...
## $ Atr38 : Factor w/ 5 levels "0","1","2","3",..: 2 5 2 4 1 3 3 5 3 2 ...
## $ Atr39 : Factor w/ 5 levels "0","1","2","3",..: 4 3 4 5 3 1 3 5 3 3 ...
## $ Atr40 : Factor w/ 5 levels "0","1","2","3",..: 4 5 4 5 2 3 4 5 3 3 ...
## $ Atr41 : Factor w/ 5 levels "0","1","2","3",..: 3 3 4 3 1 3 4 5 3 2 ...
## $ Atr42 : Factor w/ 5 levels "0","1","2","3",..: 2 3 4 3 3 2 4 5 3 3 ...
## $ Atr43 : Factor w/ 5 levels "0","1","2","3",..: 2 4 3 4 4 3 4 4 3 4 ...
## $ Atr44 : Factor w/ 5 levels "0","1","2","3",..: 3 5 4 3 1 4 5 3 3 3 ...
## $ Atr45 : Factor w/ 5 levels "0","1","2","3",..: 4 3 3 4 3 1 4 1 3 3 ...
## $ Atr46 : Factor w/ 5 levels "0","1","2","3",..: 3 3 4 3 3 3 4 1 2 3 ...
## $ Atr47 : Factor w/ 5 levels "0","1","2","3",..: 2 3 3 3 2 3 3 2 2 1 ...
## $ Atr48 : Factor w/ 5 levels "0","1","2","3",..: 4 4 4 4 3 2 4 3 2 3 ...
## $ Atr49 : Factor w/ 5 levels "0","1","2","3",..: 4 5 2 4 4 3 3 3 2 3 ...
## $ Atr50 : Factor w/ 5 levels "0","1","2","3",..: 4 5 2 4 3 2 4 3 2 3 ...
## $ Atr51 : Factor w/ 5 levels "0","1","2","3",..: 3 5 2 4 3 2 4 2 2 3 ...
## $ Atr52 : Factor w/ 5 levels "0","1","2","3",..: 4 5 3 3 3 2 3 2 2 5 ...
## $ Atr53 : Factor w/ 5 levels "0","1","2","3",..: 3 3 3 3 2 3 3 2 2 4 ...
## $ Atr54 : Factor w/ 5 levels "0","1","2","3",..: 2 3 3 3 1 1 3 1 2 4 ...
## $ Divorced: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## NULLIn the preprocessing steps, we loaded a marital dataset, renamed the “Class” column to “Divorced,” and examined the first few rows. We then converted all columns containing responses to factors, ensuring appropriate data types for subsequent analysis. This transformation is essential for categorical variables, allowing for accurate association rule mining on a dataset that explores sentiments and perceptions within marital relationships.
Analysis
EDA
Before we continue with applying the Assosiation Rules algorithm we first apply EDA. Exploratory Data Analysis is crucial in understanding and summarizing the main characteristics of a dataset.
As we can see the split in the data is almost even, we have 86 married individuals (50.5%) and 84 divorced individuals (49.5%). In this step we also want an information about each of variable distribution among the scales.
Barcharts of each of the questions
We can see the answers to the questions are mostly skewed in one or other direction. We can see some interestingly distributed answers for example question 48 - I feel right in our discussions. We can see see a very skewed distribution to the right, this results are supported by cognitive biases that suggest our brains can favor information that are already aligned with our beliefs, making us more convinced of for example of our opinion in a fight.
Assosiation Rules
Direct Correlations
In the initial phase of the analysis, a focused Apriori algorithm was executed on the entire dataset to unveil frequent itemsets and association rules. Key parameters, including a minimum support of 0.2 (how frequent the itemset is in the dataset), confidence of 0.75 (conditional probability of occurance of the item on the right hand side - consequent, given the left hand side item - antecedent), and a maximum itemset length of 2 (number of items in the rule here one antecedent and one consequent) are set, in order to see which rules have a high confidence and suggest high association between an answer to a specific question and marital status.
parameters1<- list(supp = 0.2, conf = 0.65, maxlen = 2)
rulesA1<-apriori(divorce, parameter = parameters1)## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime
## 0.65 0.1 1 none FALSE TRUE 5
## support minlen maxlen target ext
## 0.2 1 2 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 34
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[272 item(s), 170 transaction(s)] done [0.00s].
## sorting and recoding items ... [108 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2## Warning in apriori(divorce, parameter = parameters1):
## Mining stopped (maxlen reached). Only patterns up to a
## length of 2 returned!## done [0.00s].
## writing ... [2348 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].summary(rulesA1)## set of 2348 rules
##
## rule length distribution (lhs + rhs):sizes
## 1 2
## 1 2347
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1 2 2 2 2 2
##
## summary of quality measures:
## support confidence coverage
## Min. :0.2000 Min. :0.6500 Min. :0.2000
## 1st Qu.:0.2412 1st Qu.:0.7586 1st Qu.:0.2941
## Median :0.2941 Median :0.8309 Median :0.3529
## Mean :0.3045 Mean :0.8299 Mean :0.3684
## 3rd Qu.:0.3588 3rd Qu.:0.9091 3rd Qu.:0.4412
## Max. :0.6706 Max. :1.0000 Max. :1.0000
## lift count
## Min. :1.000 Min. : 34.00
## 1st Qu.:1.832 1st Qu.: 41.00
## Median :1.938 Median : 50.00
## Mean :2.119 Mean : 51.76
## 3rd Qu.:2.262 3rd Qu.: 61.00
## Max. :4.463 Max. :114.00
##
## mining info:
## data ntransactions support confidence
## divorce 170 0.2 0.65
## call
## apriori(data = divorce, parameter = parameters1)rulesD <- subset(rulesA1, subset = rhs %in% "Divorced=1")
inspect(sort(rulesD, by="confidence", decreasing = TRUE))## lhs rhs support confidence
## [1] {Atr10=3} => {Divorced=1} 0.2000000 1.0000000
## [2] {Atr16=3} => {Divorced=1} 0.2058824 1.0000000
## [3] {Atr30=3} => {Divorced=1} 0.2058824 1.0000000
## [4] {Atr24=3} => {Divorced=1} 0.2058824 1.0000000
## [5] {Atr20=3} => {Divorced=1} 0.2117647 1.0000000
## [6] {Atr26=3} => {Divorced=1} 0.2176471 1.0000000
## [7] {Atr8=3} => {Divorced=1} 0.2176471 1.0000000
## [8] {Atr14=3} => {Divorced=1} 0.2235294 1.0000000
## [9] {Atr12=3} => {Divorced=1} 0.2470588 1.0000000
## [10] {Atr25=3} => {Divorced=1} 0.2529412 1.0000000
## [11] {Atr23=3} => {Divorced=1} 0.2529412 1.0000000
## [12] {Atr29=3} => {Divorced=1} 0.2529412 1.0000000
## [13] {Atr11=3} => {Divorced=1} 0.2588235 1.0000000
## [14] {Atr18=3} => {Divorced=1} 0.2588235 1.0000000
## [15] {Atr5=3} => {Divorced=1} 0.2588235 1.0000000
## [16] {Atr27=3} => {Divorced=1} 0.2705882 1.0000000
## [17] {Atr36=4} => {Divorced=1} 0.2764706 1.0000000
## [18] {Atr21=3} => {Divorced=1} 0.2764706 1.0000000
## [19] {Atr9=3} => {Divorced=1} 0.2882353 1.0000000
## [20] {Atr19=3} => {Divorced=1} 0.2941176 1.0000000
## [21] {Atr17=3} => {Divorced=1} 0.2941176 1.0000000
## [22] {Atr15=3} => {Divorced=1} 0.3000000 1.0000000
## [23] {Atr38=4} => {Divorced=1} 0.3058824 1.0000000
## [24] {Atr35=4} => {Divorced=1} 0.3294118 1.0000000
## [25] {Atr40=4} => {Divorced=1} 0.3294118 1.0000000
## [26] {Atr41=4} => {Divorced=1} 0.3529412 1.0000000
## [27] {Atr39=4} => {Divorced=1} 0.3764706 0.9846154
## [28] {Atr54=4} => {Divorced=1} 0.3294118 0.9824561
## [29] {Atr33=4} => {Divorced=1} 0.3235294 0.9821429
## [30] {Atr34=4} => {Divorced=1} 0.2705882 0.9787234
## [31] {Atr13=3} => {Divorced=1} 0.2588235 0.9777778
## [32] {Atr7=1} => {Divorced=1} 0.2411765 0.9761905
## [33] {Atr32=4} => {Divorced=1} 0.2823529 0.9600000
## [34] {Atr44=4} => {Divorced=1} 0.2764706 0.9591837
## [35] {Atr1=3} => {Divorced=1} 0.2647059 0.9574468
## [36] {Atr37=4} => {Divorced=1} 0.3588235 0.9531250
## [37] {Atr31=4} => {Divorced=1} 0.3352941 0.9500000
## [38] {Atr50=4} => {Divorced=1} 0.3235294 0.9482759
## [39] {Atr3=3} => {Divorced=1} 0.2882353 0.9423077
## [40] {Atr51=4} => {Divorced=1} 0.2647059 0.9375000
## [41] {Atr2=3} => {Divorced=1} 0.2058824 0.9210526
## [42] {Atr42=4} => {Divorced=1} 0.2647059 0.9183673
## [43] {Atr49=4} => {Divorced=1} 0.3294118 0.9180328
## [44] {Atr53=4} => {Divorced=1} 0.2764706 0.9038462
## [45] {Atr48=4} => {Divorced=1} 0.2764706 0.8867925
## [46] {Atr47=4} => {Divorced=1} 0.3235294 0.8730159
## [47] {Atr52=4} => {Divorced=1} 0.3352941 0.8636364
## [48] {Atr43=4} => {Divorced=1} 0.3294118 0.8115942
## [49] {Atr46=4} => {Divorced=1} 0.2529412 0.7962963
## [50] {Atr45=4} => {Divorced=1} 0.2764706 0.7704918
## [51] {Atr6=1} => {Divorced=1} 0.2058824 0.7142857
## coverage lift count
## [1] 0.2000000 2.023810 34
## [2] 0.2058824 2.023810 35
## [3] 0.2058824 2.023810 35
## [4] 0.2058824 2.023810 35
## [5] 0.2117647 2.023810 36
## [6] 0.2176471 2.023810 37
## [7] 0.2176471 2.023810 37
## [8] 0.2235294 2.023810 38
## [9] 0.2470588 2.023810 42
## [10] 0.2529412 2.023810 43
## [11] 0.2529412 2.023810 43
## [12] 0.2529412 2.023810 43
## [13] 0.2588235 2.023810 44
## [14] 0.2588235 2.023810 44
## [15] 0.2588235 2.023810 44
## [16] 0.2705882 2.023810 46
## [17] 0.2764706 2.023810 47
## [18] 0.2764706 2.023810 47
## [19] 0.2882353 2.023810 49
## [20] 0.2941176 2.023810 50
## [21] 0.2941176 2.023810 50
## [22] 0.3000000 2.023810 51
## [23] 0.3058824 2.023810 52
## [24] 0.3294118 2.023810 56
## [25] 0.3294118 2.023810 56
## [26] 0.3529412 2.023810 60
## [27] 0.3823529 1.992674 64
## [28] 0.3352941 1.988304 56
## [29] 0.3294118 1.987670 55
## [30] 0.2764706 1.980750 46
## [31] 0.2647059 1.978836 44
## [32] 0.2470588 1.975624 41
## [33] 0.2941176 1.942857 48
## [34] 0.2882353 1.941205 47
## [35] 0.2764706 1.937690 45
## [36] 0.3764706 1.928943 61
## [37] 0.3529412 1.922619 57
## [38] 0.3411765 1.919130 55
## [39] 0.3058824 1.907051 49
## [40] 0.2823529 1.897321 45
## [41] 0.2235294 1.864035 35
## [42] 0.2882353 1.858601 45
## [43] 0.3588235 1.857923 56
## [44] 0.3058824 1.829212 47
## [45] 0.3117647 1.794699 47
## [46] 0.3705882 1.766818 55
## [47] 0.3882353 1.747835 57
## [48] 0.4058824 1.642512 56
## [49] 0.3176471 1.611552 43
## [50] 0.3588235 1.559329 47
## [51] 0.2882353 1.445578 35rulesM <- subset(rulesA1, subset = rhs %in% "Divorced=0")
inspect(sort(rulesM, by="confidence", decreasing = TRUE))## lhs rhs support confidence
## [1] {Atr32=0} => {Divorced=0} 0.2705882 1.0000000
## [2] {Atr3=0} => {Divorced=0} 0.3000000 1.0000000
## [3] {Atr20=0} => {Divorced=0} 0.4705882 0.9876543
## [4] {Atr18=0} => {Divorced=0} 0.4588235 0.9873418
## [5] {Atr17=0} => {Divorced=0} 0.4235294 0.9863014
## [6] {Atr40=0} => {Divorced=0} 0.4176471 0.9861111
## [7] {Atr15=0} => {Divorced=0} 0.4000000 0.9855072
## [8] {Atr1=0} => {Divorced=0} 0.4000000 0.9855072
## [9] {Atr41=0} => {Divorced=0} 0.3176471 0.9818182
## [10] {Atr39=0} => {Divorced=0} 0.2882353 0.9800000
## [11] {Atr37=0} => {Divorced=0} 0.2823529 0.9795918
## [12] {Atr42=0} => {Divorced=0} 0.2529412 0.9772727
## [13] {Atr19=0} => {Divorced=0} 0.4411765 0.9740260
## [14] {Atr4=0} => {Divorced=0} 0.4294118 0.9733333
## [15] {Atr16=0} => {Divorced=0} 0.4294118 0.9733333
## [16] {Atr30=0} => {Divorced=0} 0.4117647 0.9722222
## [17] {Atr11=0} => {Divorced=0} 0.4058824 0.9718310
## [18] {Atr10=0} => {Divorced=0} 0.3529412 0.9677419
## [19] {Atr44=0} => {Divorced=0} 0.3411765 0.9666667
## [20] {Atr2=0} => {Divorced=0} 0.3352941 0.9661017
## [21] {Atr12=0} => {Divorced=0} 0.3294118 0.9655172
## [22] {Atr9=0} => {Divorced=0} 0.4764706 0.9642857
## [23] {Atr5=0} => {Divorced=0} 0.4647059 0.9634146
## [24] {Atr29=0} => {Divorced=0} 0.4588235 0.9629630
## [25] {Atr34=0} => {Divorced=0} 0.2823529 0.9600000
## [26] {Atr26=0} => {Divorced=0} 0.4058824 0.9583333
## [27] {Atr33=0} => {Divorced=0} 0.4000000 0.9577465
## [28] {Atr13=0} => {Divorced=0} 0.2647059 0.9574468
## [29] {Atr31=0} => {Divorced=0} 0.2470588 0.9545455
## [30] {Atr14=0} => {Divorced=0} 0.3705882 0.9545455
## [31] {Atr38=0} => {Divorced=0} 0.3588235 0.9531250
## [32] {Atr8=0} => {Divorced=0} 0.4529412 0.9506173
## [33] {Atr27=0} => {Divorced=0} 0.4294118 0.9480519
## [34] {Atr24=0} => {Divorced=0} 0.4000000 0.9444444
## [35] {Atr36=0} => {Divorced=0} 0.4882353 0.9431818
## [36] {Atr21=0} => {Divorced=0} 0.4294118 0.9358974
## [37] {Atr28=0} => {Divorced=0} 0.4647059 0.9294118
## [38] {Atr35=0} => {Divorced=0} 0.4647059 0.9294118
## [39] {Atr25=0} => {Divorced=0} 0.3411765 0.9206349
## [40] {Atr54=0} => {Divorced=0} 0.2705882 0.9200000
## [41] {Atr22=0} => {Divorced=0} 0.4705882 0.9195402
## [42] {Atr23=0} => {Divorced=0} 0.4764706 0.9000000
## [43] {Atr48=2} => {Divorced=0} 0.2470588 0.8936170
## [44] {Atr51=2} => {Divorced=0} 0.2235294 0.8837209
## [45] {Atr7=0} => {Divorced=0} 0.5000000 0.7456140
## [46] {Atr6=0} => {Divorced=0} 0.3764706 0.7441860
## coverage lift count
## [1] 0.2705882 1.976744 46
## [2] 0.3000000 1.976744 51
## [3] 0.4764706 1.952340 80
## [4] 0.4647059 1.951722 78
## [5] 0.4294118 1.949665 72
## [6] 0.4235294 1.949289 71
## [7] 0.4058824 1.948096 68
## [8] 0.4058824 1.948096 68
## [9] 0.3235294 1.940803 54
## [10] 0.2941176 1.937209 49
## [11] 0.2882353 1.936402 48
## [12] 0.2588235 1.931818 43
## [13] 0.4529412 1.925400 75
## [14] 0.4411765 1.924031 73
## [15] 0.4411765 1.924031 73
## [16] 0.4235294 1.921835 70
## [17] 0.4176471 1.921061 69
## [18] 0.3647059 1.912978 60
## [19] 0.3529412 1.910853 58
## [20] 0.3470588 1.909736 57
## [21] 0.3411765 1.908581 56
## [22] 0.4941176 1.906146 81
## [23] 0.4823529 1.904424 79
## [24] 0.4764706 1.903531 78
## [25] 0.2941176 1.897674 48
## [26] 0.4235294 1.894380 69
## [27] 0.4176471 1.893220 68
## [28] 0.2764706 1.892627 45
## [29] 0.2588235 1.886892 42
## [30] 0.3882353 1.886892 63
## [31] 0.3764706 1.884084 61
## [32] 0.4764706 1.879127 77
## [33] 0.4529412 1.874056 73
## [34] 0.4235294 1.866925 68
## [35] 0.5176471 1.864429 83
## [36] 0.4588235 1.850030 73
## [37] 0.5000000 1.837209 79
## [38] 0.5000000 1.837209 79
## [39] 0.3705882 1.819860 58
## [40] 0.2941176 1.818605 46
## [41] 0.5117647 1.817696 80
## [42] 0.5294118 1.779070 81
## [43] 0.2764706 1.766452 42
## [44] 0.2529412 1.746890 38
## [45] 0.6705882 1.473888 85
## [46] 0.5058824 1.471065 64As we can see in the divorced data set we have 26 rules with confidence level of 1 for divorced individuals and 2 rules with confidence of 1 for married individuals. It means that more specific answers on the scale are directly assosiated with being divorced than with being married. Let’s now look at those rules in order of how frequently they occur.
rulesD1 <- subset(rulesA1, subset = rhs %in% "Divorced=1"& confidence == 1 | rhs %in% "Divorced=0" & confidence == 1)
inspect(sort(rulesD1, by="support", decreasing = TRUE))## lhs rhs support confidence
## [1] {Atr41=4} => {Divorced=1} 0.3529412 1
## [2] {Atr35=4} => {Divorced=1} 0.3294118 1
## [3] {Atr40=4} => {Divorced=1} 0.3294118 1
## [4] {Atr38=4} => {Divorced=1} 0.3058824 1
## [5] {Atr15=3} => {Divorced=1} 0.3000000 1
## [6] {Atr3=0} => {Divorced=0} 0.3000000 1
## [7] {Atr19=3} => {Divorced=1} 0.2941176 1
## [8] {Atr17=3} => {Divorced=1} 0.2941176 1
## [9] {Atr9=3} => {Divorced=1} 0.2882353 1
## [10] {Atr36=4} => {Divorced=1} 0.2764706 1
## [11] {Atr21=3} => {Divorced=1} 0.2764706 1
## [12] {Atr27=3} => {Divorced=1} 0.2705882 1
## [13] {Atr32=0} => {Divorced=0} 0.2705882 1
## [14] {Atr11=3} => {Divorced=1} 0.2588235 1
## [15] {Atr18=3} => {Divorced=1} 0.2588235 1
## [16] {Atr5=3} => {Divorced=1} 0.2588235 1
## [17] {Atr25=3} => {Divorced=1} 0.2529412 1
## [18] {Atr23=3} => {Divorced=1} 0.2529412 1
## [19] {Atr29=3} => {Divorced=1} 0.2529412 1
## [20] {Atr12=3} => {Divorced=1} 0.2470588 1
## [21] {Atr14=3} => {Divorced=1} 0.2235294 1
## [22] {Atr26=3} => {Divorced=1} 0.2176471 1
## [23] {Atr8=3} => {Divorced=1} 0.2176471 1
## [24] {Atr20=3} => {Divorced=1} 0.2117647 1
## [25] {Atr16=3} => {Divorced=1} 0.2058824 1
## [26] {Atr30=3} => {Divorced=1} 0.2058824 1
## [27] {Atr24=3} => {Divorced=1} 0.2058824 1
## [28] {Atr10=3} => {Divorced=1} 0.2000000 1
## coverage lift count
## [1] 0.3529412 2.023810 60
## [2] 0.3294118 2.023810 56
## [3] 0.3294118 2.023810 56
## [4] 0.3058824 2.023810 52
## [5] 0.3000000 2.023810 51
## [6] 0.3000000 1.976744 51
## [7] 0.2941176 2.023810 50
## [8] 0.2941176 2.023810 50
## [9] 0.2882353 2.023810 49
## [10] 0.2764706 2.023810 47
## [11] 0.2764706 2.023810 47
## [12] 0.2705882 2.023810 46
## [13] 0.2705882 1.976744 46
## [14] 0.2588235 2.023810 44
## [15] 0.2588235 2.023810 44
## [16] 0.2588235 2.023810 44
## [17] 0.2529412 2.023810 43
## [18] 0.2529412 2.023810 43
## [19] 0.2529412 2.023810 43
## [20] 0.2470588 2.023810 42
## [21] 0.2235294 2.023810 38
## [22] 0.2176471 2.023810 37
## [23] 0.2176471 2.023810 37
## [24] 0.2117647 2.023810 36
## [25] 0.2058824 2.023810 35
## [26] 0.2058824 2.023810 35
## [27] 0.2058824 2.023810 35
## [28] 0.2000000 2.023810 34atrDiv <- c("Atr41","Atr40","Atr35","Atr38","Atr15","Atr32","Atr3")
plots <- list()
for (attribute in atrDiv) {
gg<- divorce %>%
ggplot(aes(x = factor(!!sym(attribute)), fill = Divorced)) +
geom_bar(position = "dodge", color = "black", show.legend = T) +
labs(title = paste(attribute, "by Divorce Status"),
x = attribute , y = "") +
theme_minimal()
plots[[attribute]] <- gg
}
grid.arrange(grobs = plots, ncol = 3)
I visualized some of the most frequent rules above to help the interpretation: Questions where an answer 4 is directly assosiated with being divorced. - Question 41 - When I talk to my wife about something, my calm suddenly breaks - Question 35 - I can insult our discussions. - Question 38 - I hate my wife’s way of bringing it up. Questions where an answer 3 or 4 is directly assosiated with being divorced - Question 40 - We’re just starting a fight before I know what’s going on. - Question 15 - Our dreams of living with my wife are similar and harmonious. Questions where an answer 0 is directly assosiated with being married - Question 3 - When we need it, we can take our discussions with my wife from the beginning and correct it. - Question 32 - When discussing with my wife, I usually use expressions such as as ‘you always’ or ‘you never’ Those questions show the direct correlation between the specific answer to the question and the marriage status, so any further rules containing those specific answers will suggest the same assosiation in marrige status, in order to avoid redundance and to find more complex rules I will remove those specific answers to attributes and run a general Apriori algorithm again.
General Rules
Here we set the key parameters in the same manner as we did before, including a minimum support of 0.2, confidence of 0.65, but increasing the maximum itemset length of 5, minimum itemset length of 2. The last two parameters were chosen to strike a balance between pattern identification and computational efficiency. This decision to restrict the maxlen parameter to 5 aimed to address potential computational constraints. The max number of rules scales exponentially with the number of unique variables. Since here we have 272 variables we have to restrict our length and hyper parameters to draw meaningful conclusions. While the minum length is provided to exclude the rules with the empty lhs. The subsequent summary provides an overview of the generated association rules and associated quality measures.
# Getting the list of specific lhs from previous step, where the confidence was equal to 1
lhs_list <- as(lhs(rulesD1), "list")
lhs_char <- as.character(lhs_list)
# Exclude rules with specific LHS values - the ones we previously noted with confidence 1
parameters1 <- list(supp = 0.2, conf = 0.65, minlen = 2, maxlen = 5)
rulesA <- apriori(divorce, parameter = parameters1,appearance = list(none = lhs_char))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime
## 0.65 0.1 1 none FALSE TRUE 5
## support minlen maxlen target ext
## 0.2 2 5 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 34
##
## set item appearances ...[28 item(s)] done [0.00s].
## set transactions ...[272 item(s), 170 transaction(s)] done [0.00s].
## sorting and recoding items ... [80 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5## Warning in apriori(divorce, parameter = parameters1,
## appearance = list(none = lhs_char)): Mining stopped (maxlen
## reached). Only patterns up to a length of 5 returned!## done [0.07s].
## writing ... [1712037 rule(s)] done [0.20s].
## creating S4 object ... done [0.67s].summary(rulesA)## set of 1712037 rules
##
## rule length distribution (lhs + rhs):sizes
## 2 3 4 5
## 1765 28405 251517 1430350
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.000 5.000 5.000 4.817 5.000 5.000
##
## summary of quality measures:
## support confidence coverage
## Min. :0.2000 Min. :0.6500 Min. :0.2000
## 1st Qu.:0.2176 1st Qu.:0.8444 1st Qu.:0.2412
## Median :0.2353 Median :0.9149 Median :0.2706
## Mean :0.2475 Mean :0.8945 Mean :0.2788
## 3rd Qu.:0.2706 3rd Qu.:0.9592 3rd Qu.:0.3118
## Max. :0.5000 Max. :1.0000 Max. :0.6706
## lift count
## Min. :1.266 Min. :34.00
## 1st Qu.:1.883 1st Qu.:37.00
## Median :1.977 Median :40.00
## Mean :2.010 Mean :42.08
## 3rd Qu.:2.092 3rd Qu.:46.00
## Max. :3.949 Max. :85.00
##
## mining info:
## data ntransactions support confidence
## divorce 170 0.2 0.65
## call
## apriori(data = divorce, parameter = parameters1, appearance = list(none = lhs_char))set.seed(77)
plot(rulesA, method = "graph", measure = "support", shading = "lift", main = "Association Rules Graph")## Warning: Unknown control parameters: main## Available control parameters (with default values):
## layout = stress
## circular = FALSE
## ggraphdots = NULL
## edges = <environment>
## nodes = <environment>
## nodetext = <environment>
## colors = c("#EE0000FF", "#EEEEEEFF")
## engine = ggplot2
## max = 100
## verbose = FALSE## Warning: Too many rules supplied. Only plotting the best
## 100 using 'lift' (change control parameter max if needed).
Below, efforts were made to improve the interpretability of the association rules graph by restricting the rules based on quality measures. The plot function was initially used to create a graph, but due to the high number of rules, the visualization became challenging to interpret. To address this, rules were filtered based on a combination of high confidence, lift, and support, specifically looking for rules where the ‘Divorced’ variable is in the consequent. The level of each quality measure was aproximated based on the summary of the rules above the mean/median level. These refined subsets of rules aim to provide clearer insights into the associations involving the ‘Divorced’ variable while enhancing the interpretability of the analysis.
# Filtering the dataset by the quality measures
best_rules <- subset(rulesA, confidence > 0.89 & lift > 2 & support > 0.24)
# Looking for rules that have the the divorced variable as consequent
rules_related <- subset(best_rules, subset = rhs %in% "Divorced=1"|rhs %in% "Divorced=0")
inspect(head(sort(rules_related, by="support", decreasing = TRUE),n=100))## lhs rhs support confidence coverage lift count
## [1] {Atr37=4,
## Atr39=4} => {Divorced=1} 0.3470588 1 0.3470588 2.02381 59
## [2] {Atr39=4,
## Atr54=4} => {Divorced=1} 0.3294118 1 0.3294118 2.02381 56
## [3] {Atr33=4,
## Atr49=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [4] {Atr33=4,
## Atr43=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [5] {Atr37=4,
## Atr54=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [6] {Atr31=4,
## Atr39=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [7] {Atr31=4,
## Atr43=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [8] {Atr39=4,
## Atr47=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [9] {Atr39=4,
## Atr43=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [10] {Atr33=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [11] {Atr37=4,
## Atr39=4,
## Atr54=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [12] {Atr39=4,
## Atr43=4,
## Atr47=4} => {Divorced=1} 0.3235294 1 0.3235294 2.02381 55
## [13] {Atr33=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [14] {Atr33=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [15] {Atr33=4,
## Atr39=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [16] {Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [17] {Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [18] {Atr43=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [19] {Atr31=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [20] {Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [21] {Atr39=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [22] {Atr43=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [23] {Atr31=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [24] {Atr31=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [25] {Atr37=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [26] {Atr39=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [27] {Atr49=4,
## Atr52=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [28] {Atr37=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [29] {Atr33=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [30] {Atr33=4,
## Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [31] {Atr33=4,
## Atr39=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [32] {Atr33=4,
## Atr43=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [33] {Atr31=4,
## Atr33=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [34] {Atr31=4,
## Atr33=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [35] {Atr33=4,
## Atr47=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [36] {Atr33=4,
## Atr37=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [37] {Atr33=4,
## Atr39=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [38] {Atr33=4,
## Atr39=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [39] {Atr33=4,
## Atr43=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [40] {Atr33=4,
## Atr37=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [41] {Atr33=4,
## Atr39=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [42] {Atr47=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [43] {Atr39=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [44] {Atr43=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [45] {Atr39=4,
## Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [46] {Atr43=4,
## Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [47] {Atr39=4,
## Atr43=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [48] {Atr31=4,
## Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [49] {Atr31=4,
## Atr39=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [50] {Atr31=4,
## Atr43=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [51] {Atr39=4,
## Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [52] {Atr43=4,
## Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [53] {Atr39=4,
## Atr43=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [54] {Atr31=4,
## Atr37=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [55] {Atr31=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [56] {Atr31=4,
## Atr39=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [57] {Atr31=4,
## Atr43=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [58] {Atr31=4,
## Atr37=4,
## Atr39=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [59] {Atr31=4,
## Atr37=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [60] {Atr31=4,
## Atr39=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [61] {Atr39=4,
## Atr47=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [62] {Atr37=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [63] {Atr39=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [64] {Atr33=4,
## Atr47=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [65] {Atr33=4,
## Atr39=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [66] {Atr33=4,
## Atr43=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [67] {Atr33=4,
## Atr39=4,
## Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [68] {Atr33=4,
## Atr43=4,
## Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [69] {Atr33=4,
## Atr39=4,
## Atr43=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [70] {Atr31=4,
## Atr33=4,
## Atr37=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [71] {Atr31=4,
## Atr33=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [72] {Atr31=4,
## Atr33=4,
## Atr37=4,
## Atr43=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [73] {Atr33=4,
## Atr39=4,
## Atr47=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [74] {Atr33=4,
## Atr43=4,
## Atr47=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [75] {Atr33=4,
## Atr37=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [76] {Atr33=4,
## Atr39=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [77] {Atr33=4,
## Atr39=4,
## Atr43=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [78] {Atr39=4,
## Atr47=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [79] {Atr43=4,
## Atr47=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [80] {Atr39=4,
## Atr43=4,
## Atr49=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [81] {Atr39=4,
## Atr43=4,
## Atr47=4,
## Atr54=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [82] {Atr31=4,
## Atr39=4,
## Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [83] {Atr31=4,
## Atr43=4,
## Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [84] {Atr31=4,
## Atr39=4,
## Atr43=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [85] {Atr39=4,
## Atr43=4,
## Atr47=4,
## Atr50=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [86] {Atr31=4,
## Atr37=4,
## Atr43=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [87] {Atr31=4,
## Atr39=4,
## Atr43=4,
## Atr47=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [88] {Atr39=4,
## Atr43=4,
## Atr47=4,
## Atr49=4} => {Divorced=1} 0.3176471 1 0.3176471 2.02381 54
## [89] {Atr33=4,
## Atr50=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [90] {Atr33=4,
## Atr52=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [91] {Atr50=4,
## Atr54=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [92] {Atr31=4,
## Atr54=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [93] {Atr52=4,
## Atr54=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [94] {Atr37=4,
## Atr50=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [95] {Atr37=4,
## Atr47=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [96] {Atr33=4,
## Atr50=4,
## Atr54=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [97] {Atr31=4,
## Atr33=4,
## Atr54=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [98] {Atr33=4,
## Atr37=4,
## Atr54=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [99] {Atr31=4,
## Atr33=4,
## Atr50=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53
## [100] {Atr33=4,
## Atr49=4,
## Atr50=4} => {Divorced=1} 0.3117647 1 0.3117647 2.02381 53#As they are no rules with rhs are Divorced=0 with the previous quality measures we lower the lift that causes the exclusion
rules_relatedM <- subset(rulesA, subset = rhs %in% "Divorced=0" & confidence > 0.89 & support > 0.24 & lift > 1.9)
inspect(head(sort(rules_relatedM, by="support", decreasing = TRUE),n=100))## lhs rhs support confidence coverage lift count
## [1] {Atr7=0,
## Atr36=0} => {Divorced=0} 0.4823529 0.9761905 0.4941176 1.929679 82
## [2] {Atr9=0} => {Divorced=0} 0.4764706 0.9642857 0.4941176 1.906146 81
## [3] {Atr20=0} => {Divorced=0} 0.4705882 0.9876543 0.4764706 1.952340 80
## [4] {Atr7=0,
## Atr9=0} => {Divorced=0} 0.4705882 0.9638554 0.4882353 1.905296 80
## [5] {Atr5=0} => {Divorced=0} 0.4647059 0.9634146 0.4823529 1.904424 79
## [6] {Atr7=0,
## Atr20=0} => {Divorced=0} 0.4647059 0.9875000 0.4705882 1.952035 79
## [7] {Atr18=0} => {Divorced=0} 0.4588235 0.9873418 0.4647059 1.951722 78
## [8] {Atr29=0} => {Divorced=0} 0.4588235 0.9629630 0.4764706 1.903531 78
## [9] {Atr5=0,
## Atr7=0} => {Divorced=0} 0.4588235 0.9750000 0.4705882 1.927326 78
## [10] {Atr9=0,
## Atr36=0} => {Divorced=0} 0.4588235 0.9873418 0.4647059 1.951722 78
## [11] {Atr7=0,
## Atr28=0} => {Divorced=0} 0.4588235 0.9629630 0.4764706 1.903531 78
## [12] {Atr22=0,
## Atr36=0} => {Divorced=0} 0.4588235 0.9629630 0.4764706 1.903531 78
## [13] {Atr23=0,
## Atr36=0} => {Divorced=0} 0.4588235 0.9629630 0.4764706 1.903531 78
## [14] {Atr7=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4588235 0.9750000 0.4705882 1.927326 78
## [15] {Atr7=0,
## Atr18=0} => {Divorced=0} 0.4529412 0.9871795 0.4588235 1.951401 77
## [16] {Atr20=0,
## Atr36=0} => {Divorced=0} 0.4529412 0.9871795 0.4588235 1.951401 77
## [17] {Atr8=0,
## Atr9=0} => {Divorced=0} 0.4529412 0.9625000 0.4705882 1.902616 77
## [18] {Atr7=0,
## Atr29=0} => {Divorced=0} 0.4529412 0.9746835 0.4647059 1.926700 77
## [19] {Atr9=0,
## Atr22=0} => {Divorced=0} 0.4529412 0.9625000 0.4705882 1.902616 77
## [20] {Atr9=0,
## Atr23=0} => {Divorced=0} 0.4529412 0.9625000 0.4705882 1.902616 77
## [21] {Atr7=0,
## Atr9=0,
## Atr36=0} => {Divorced=0} 0.4529412 0.9871795 0.4588235 1.951401 77
## [22] {Atr7=0,
## Atr22=0,
## Atr36=0} => {Divorced=0} 0.4529412 0.9746835 0.4647059 1.926700 77
## [23] {Atr7=0,
## Atr23=0,
## Atr36=0} => {Divorced=0} 0.4529412 0.9746835 0.4647059 1.926700 77
## [24] {Atr20=0,
## Atr23=0} => {Divorced=0} 0.4470588 0.9870130 0.4529412 1.951072 76
## [25] {Atr7=0,
## Atr8=0} => {Divorced=0} 0.4470588 0.9620253 0.4647059 1.901678 76
## [26] {Atr5=0,
## Atr9=0} => {Divorced=0} 0.4470588 0.9743590 0.4588235 1.926058 76
## [27] {Atr5=0,
## Atr36=0} => {Divorced=0} 0.4470588 1.0000000 0.4470588 1.976744 76
## [28] {Atr28=0,
## Atr36=0} => {Divorced=0} 0.4470588 0.9870130 0.4529412 1.951072 76
## [29] {Atr7=0,
## Atr20=0,
## Atr36=0} => {Divorced=0} 0.4470588 0.9870130 0.4529412 1.951072 76
## [30] {Atr7=0,
## Atr8=0,
## Atr9=0} => {Divorced=0} 0.4470588 0.9620253 0.4647059 1.901678 76
## [31] {Atr7=0,
## Atr9=0,
## Atr22=0} => {Divorced=0} 0.4470588 0.9620253 0.4647059 1.901678 76
## [32] {Atr7=0,
## Atr9=0,
## Atr23=0} => {Divorced=0} 0.4470588 0.9620253 0.4647059 1.901678 76
## [33] {Atr19=0} => {Divorced=0} 0.4411765 0.9740260 0.4529412 1.925400 75
## [34] {Atr18=0,
## Atr36=0} => {Divorced=0} 0.4411765 1.0000000 0.4411765 1.976744 75
## [35] {Atr9=0,
## Atr20=0} => {Divorced=0} 0.4411765 1.0000000 0.4411765 1.976744 75
## [36] {Atr8=0,
## Atr23=0} => {Divorced=0} 0.4411765 0.9615385 0.4588235 1.900716 75
## [37] {Atr28=0,
## Atr29=0} => {Divorced=0} 0.4411765 0.9615385 0.4588235 1.900716 75
## [38] {Atr29=0,
## Atr36=0} => {Divorced=0} 0.4411765 1.0000000 0.4411765 1.976744 75
## [39] {Atr7=0,
## Atr20=0,
## Atr23=0} => {Divorced=0} 0.4411765 0.9868421 0.4470588 1.950734 75
## [40] {Atr8=0,
## Atr9=0,
## Atr23=0} => {Divorced=0} 0.4411765 0.9615385 0.4588235 1.900716 75
## [41] {Atr5=0,
## Atr7=0,
## Atr9=0} => {Divorced=0} 0.4411765 0.9740260 0.4529412 1.925400 75
## [42] {Atr5=0,
## Atr7=0,
## Atr36=0} => {Divorced=0} 0.4411765 1.0000000 0.4411765 1.976744 75
## [43] {Atr9=0,
## Atr22=0,
## Atr36=0} => {Divorced=0} 0.4411765 0.9868421 0.4470588 1.950734 75
## [44] {Atr7=0,
## Atr28=0,
## Atr36=0} => {Divorced=0} 0.4411765 1.0000000 0.4411765 1.976744 75
## [45] {Atr22=0,
## Atr23=0,
## Atr36=0} => {Divorced=0} 0.4411765 0.9740260 0.4529412 1.925400 75
## [46] {Atr7=0,
## Atr19=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [47] {Atr18=0,
## Atr20=0} => {Divorced=0} 0.4352941 1.0000000 0.4352941 1.976744 74
## [48] {Atr5=0,
## Atr18=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [49] {Atr9=0,
## Atr18=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [50] {Atr18=0,
## Atr23=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [51] {Atr5=0,
## Atr20=0} => {Divorced=0} 0.4352941 1.0000000 0.4352941 1.976744 74
## [52] {Atr20=0,
## Atr28=0} => {Divorced=0} 0.4352941 1.0000000 0.4352941 1.976744 74
## [53] {Atr20=0,
## Atr22=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [54] {Atr8=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [55] {Atr5=0,
## Atr22=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [56] {Atr5=0,
## Atr23=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [57] {Atr9=0,
## Atr35=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [58] {Atr9=0,
## Atr28=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [59] {Atr7=0,
## Atr18=0,
## Atr36=0} => {Divorced=0} 0.4352941 1.0000000 0.4352941 1.976744 74
## [60] {Atr7=0,
## Atr9=0,
## Atr20=0} => {Divorced=0} 0.4352941 1.0000000 0.4352941 1.976744 74
## [61] {Atr8=0,
## Atr9=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [62] {Atr7=0,
## Atr28=0,
## Atr29=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [63] {Atr7=0,
## Atr29=0,
## Atr36=0} => {Divorced=0} 0.4352941 1.0000000 0.4352941 1.976744 74
## [64] {Atr9=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [65] {Atr9=0,
## Atr23=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [66] {Atr23=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [67] {Atr7=0,
## Atr9=0,
## Atr22=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9866667 0.4411765 1.950388 74
## [68] {Atr7=0,
## Atr22=0,
## Atr23=0,
## Atr36=0} => {Divorced=0} 0.4352941 0.9736842 0.4470588 1.924725 74
## [69] {Atr4=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [70] {Atr16=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [71] {Atr18=0,
## Atr22=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [72] {Atr20=0,
## Atr29=0} => {Divorced=0} 0.4294118 1.0000000 0.4294118 1.976744 73
## [73] {Atr20=0,
## Atr35=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [74] {Atr9=0,
## Atr29=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [75] {Atr7=0,
## Atr18=0,
## Atr20=0} => {Divorced=0} 0.4294118 1.0000000 0.4294118 1.976744 73
## [76] {Atr5=0,
## Atr7=0,
## Atr18=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [77] {Atr7=0,
## Atr9=0,
## Atr18=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [78] {Atr7=0,
## Atr18=0,
## Atr23=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [79] {Atr5=0,
## Atr7=0,
## Atr20=0} => {Divorced=0} 0.4294118 1.0000000 0.4294118 1.976744 73
## [80] {Atr20=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [81] {Atr7=0,
## Atr20=0,
## Atr28=0} => {Divorced=0} 0.4294118 1.0000000 0.4294118 1.976744 73
## [82] {Atr7=0,
## Atr20=0,
## Atr22=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [83] {Atr20=0,
## Atr23=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [84] {Atr7=0,
## Atr8=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [85] {Atr7=0,
## Atr23=0,
## Atr29=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [86] {Atr5=0,
## Atr9=0,
## Atr36=0} => {Divorced=0} 0.4294118 1.0000000 0.4294118 1.976744 73
## [87] {Atr5=0,
## Atr7=0,
## Atr22=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [88] {Atr5=0,
## Atr7=0,
## Atr23=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [89] {Atr7=0,
## Atr9=0,
## Atr35=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [90] {Atr7=0,
## Atr9=0,
## Atr28=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [91] {Atr7=0,
## Atr22=0,
## Atr28=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [92] {Atr7=0,
## Atr8=0,
## Atr9=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [93] {Atr7=0,
## Atr9=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [94] {Atr7=0,
## Atr9=0,
## Atr23=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9864865 0.4352941 1.950031 73
## [95] {Atr7=0,
## Atr22=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [96] {Atr7=0,
## Atr23=0,
## Atr35=0,
## Atr36=0} => {Divorced=0} 0.4294118 0.9733333 0.4411765 1.924031 73
## [97] {Atr17=0} => {Divorced=0} 0.4235294 0.9863014 0.4294118 1.949665 72
## [98] {Atr4=0,
## Atr7=0} => {Divorced=0} 0.4235294 0.9863014 0.4294118 1.949665 72
## [99] {Atr7=0,
## Atr16=0} => {Divorced=0} 0.4235294 0.9729730 0.4352941 1.923319 72
## [100] {Atr7=0,
## Atr27=0} => {Divorced=0} 0.4235294 0.9729730 0.4352941 1.923319 72Rules with ‘Divorced = 1’ as the Consequent: Similarly to before we have a lot of rules with confidence level equal to 1, meaning the occurrence of them in the survey meant a divorced individual. Interestingly basing on the first 10 most frequent rules we can see that the rules have a lot to do with extremes as they are all at the level of 4. Taking on the first pair we can see that the individuals that highly agreed with the statements that the arguments with their spouses often start unexpectedly and are not calm were also divorced. Most of those questions address fighting and communicating with more polarising answers. So the high association to the status of being divorced is confirming the general societal expectation of what proceeds a break up of a relationship.
Rules with ‘Divorced = 0’ as the Consequent (Married Individuals): In contrast to the previously mentioned rules the ones that have as a consequent being married don’t all have as high confidance level as the ones for divorced individuals but with the lowered lift (marginally lowered lift, still a positive association) they have a much better support levels. The top rules here are consisted with answers on the scale at the level of 0 and the questions are more postively framed, for example questions about having common values or enjoying time spend together. This also aligns with what one would expect from a long lasting relationship.
In summary: The analysis highlights specific attributes related to arguments that are strongly associated with divorce, providing valuable insights into potential contributing factors for marital challenges. Similarly, certain attributes indicate stability in marriages, emphasizing the importance of effective communication, interest in the partner and conflict resolution.
Subgroups
As we delve further into the analysis, the rationale behind separating the dataset based on divorce status becomes more evident. By isolating divorced and married individuals, we can possibly gain a more refined perspective, making interpretation more straightforward and meaningful. This approach allows for focused analyses on distinct patterns and associations unique to each group. Dividing the dataset not only enhances interpretability but also opens avenues for a more nuanced understanding of factors contributing to marital outcomes. This strategic division sets the stage for targeted interventions or insights tailored to the specific dynamics within each subgroup.
parameters2<- list(supp = 0.2, conf = 0.65, minlen = 2, maxlen = 5)
divorced_data <- subset(divorce, Divorced == 1)
married_data <- subset(divorce, Divorced == 0)
#removing the column about the marital status
divorced_data <- divorced_data[,1:54]
married_data <- married_data[,1:54]
# For divorced individuals
rules_divorced <- apriori(divorced_data, parameter = parameters2)## Warning in apriori(divorced_data, parameter = parameters2):
## Mining stopped (maxlen reached). Only patterns up to a
## length of 5 returned!# For married individuals
rules_married <- apriori(married_data, parameter = parameters2)## Warning in apriori(married_data, parameter = parameters2):
## Mining stopped (maxlen reached). Only patterns up to a
## length of 5 returned!summary(rules_divorced)## set of 5106520 rules
##
## rule length distribution (lhs + rhs):sizes
## 2 3 4 5
## 2151 48382 562060 4493927
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.00 5.00 5.00 4.87 5.00 5.00
##
## summary of quality measures:
## support confidence coverage
## Min. :0.2024 Min. :0.6500 Min. :0.2024
## 1st Qu.:0.2143 1st Qu.:0.9130 1st Qu.:0.2262
## Median :0.2500 Median :1.0000 Median :0.2738
## Mean :0.2681 Mean :0.9438 Mean :0.2867
## 3rd Qu.:0.3095 3rd Qu.:1.0000 3rd Qu.:0.3214
## Max. :0.7024 Max. :1.0000 Max. :0.7619
## lift count
## Min. :0.8906 Min. :17.00
## 1st Qu.:1.4000 1st Qu.:18.00
## Median :1.5273 Median :21.00
## Mean :1.6675 Mean :22.52
## 3rd Qu.:1.8261 3rd Qu.:26.00
## Max. :4.4211 Max. :59.00
##
## mining info:
## data ntransactions support confidence
## divorced_data 84 0.2 0.65
## call
## apriori(data = divorced_data, parameter = parameters2)summary(rules_married)## set of 5201922 rules
##
## rule length distribution (lhs + rhs):sizes
## 2 3 4 5
## 2344 49670 576599 4573309
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.000 5.000 5.000 4.869 5.000 5.000
##
## summary of quality measures:
## support confidence coverage
## Min. :0.2093 Min. :0.6500 Min. :0.2093
## 1st Qu.:0.2442 1st Qu.:0.8158 1st Qu.:0.2791
## Median :0.3023 Median :0.9000 Median :0.3605
## Mean :0.3337 Mean :0.8778 Mean :0.3833
## 3rd Qu.:0.3953 3rd Qu.:0.9524 3rd Qu.:0.4651
## Max. :0.9535 Max. :1.0000 Max. :0.9884
## lift count
## Min. :0.7633 Min. :18.0
## 1st Qu.:1.0067 1st Qu.:21.0
## Median :1.0492 Median :26.0
## Mean :1.0718 Mean :28.7
## 3rd Qu.:1.1128 3rd Qu.:34.0
## Max. :2.6282 Max. :82.0
##
## mining info:
## data ntransactions support confidence
## married_data 86 0.2 0.65
## call
## apriori(data = married_data, parameter = parameters2)rulesDconf <- sort(rules_divorced, by="confidence", decreasing = TRUE)
inspect(head(rulesDconf))## lhs rhs support confidence coverage
## [1] {Atr8=4} => {Atr2=4} 0.2500000 1 0.2500000
## [2] {Atr18=4} => {Atr2=4} 0.2500000 1 0.2500000
## [3] {Atr23=4} => {Atr29=4} 0.2619048 1 0.2619048
## [4] {Atr23=4} => {Atr25=4} 0.2619048 1 0.2619048
## [5] {Atr23=4} => {Atr5=4} 0.2619048 1 0.2619048
## [6] {Atr23=4} => {Atr17=4} 0.2619048 1 0.2619048
## lift count
## [1] 3.818182 21
## [2] 3.818182 21
## [3] 3.652174 22
## [4] 3.500000 22
## [5] 3.230769 22
## [6] 3.230769 22rulesMconf <- sort(rules_married, by="confidence", decreasing = TRUE)
inspect(head(rulesMconf))## lhs rhs support confidence coverage
## [1] {Atr53=2} => {Atr27=0} 0.2093023 1 0.2093023
## [2] {Atr53=2} => {Atr29=0} 0.2093023 1 0.2093023
## [3] {Atr53=2} => {Atr28=0} 0.2093023 1 0.2093023
## [4] {Atr53=2} => {Atr23=0} 0.2093023 1 0.2093023
## [5] {Atr53=2} => {Atr9=0} 0.2093023 1 0.2093023
## [6] {Atr53=2} => {Atr7=0} 0.2093023 1 0.2093023
## lift count
## [1] 1.178082 18
## [2] 1.102564 18
## [3] 1.088608 18
## [4] 1.061728 18
## [5] 1.061728 18
## [6] 1.011765 18In scrutinizing the outcomes of the Apriori analysis on divorced and married individuals, we observe a wealth of association rules. To enhance interpretability, I opted to narrow down the results by creating subsets based on quality measures. In both subsets, confidence levels are notably high, exceeding 90% for married individuals and reaching 100% for divorced individuals. The lift metric, indicative of the strength of association, was set substantially higher than the third quartile to ensure a focused and meaningful subset of rules. This strategic filtering resulted in subsets that capture the most robust and reliable patterns within each group, providing a more manageable and insightful set of association rules for further exploration.
best_rules_divorced <- subset(rules_divorced, confidence > 0.94 & lift > 2 & support > 0.25 )
best_rules_married <- subset(rules_married, confidence > 0.9 & lift > 1.5 & support > 0.3 )plot(best_rules_divorced, method = "graph", measure = "support", shading = "lift", limit=20, main = "Association Rules Graph- Divorced",type = "itemsets")## Warning: Unknown control parameters: main, type## Available control parameters (with default values):
## layout = stress
## circular = FALSE
## ggraphdots = NULL
## edges = <environment>
## nodes = <environment>
## nodetext = <environment>
## colors = c("#EE0000FF", "#EEEEEEFF")
## engine = ggplot2
## max = 100
## verbose = FALSE
plot(best_rules_married, method = "graph", measure = "support", shading = "lift",limit=20, main = "Association Rules Graph- Married", type = "itemsets")## Warning: Unknown control parameters: main, type## Available control parameters (with default values):
## layout = stress
## circular = FALSE
## ggraphdots = NULL
## edges = <environment>
## nodes = <environment>
## nodetext = <environment>
## colors = c("#EE0000FF", "#EEEEEEFF")
## engine = ggplot2
## max = 100
## verbose = FALSE
In this phase of the analysis, the focus shifts to identifying the most significant association rules within the divorced and married subgroups. By applying stringent criteria based on confidence, lift, support, and coverage (based on previously seen summaries), subsets of high-quality rules are generated for both groups. These refined subsets capture the most robust patterns while minimizing noise in the visualization. The graphing process, however, encounters challenges due to the overlap of rules, prompting consideration for adjustments within the plot function to enhance clarity and reduce the number of rules plotted. Even though the plots are much more interpretable than the previous ones. In order to find the most meaningful assosiations I again inspect the best rules of each subset.
bestrulesDconf <- sort(best_rules_divorced, by="support", decreasing = TRUE)
inspect(head(bestrulesDconf),n=300)## lhs rhs support confidence
## [1] {Atr5=3, Atr29=3} => {Atr7=1} 0.4761905 1
## [2] {Atr13=3, Atr29=3} => {Atr7=1} 0.4761905 1
## [3] {Atr1=3, Atr29=3} => {Atr7=1} 0.4761905 1
## [4] {Atr5=3, Atr25=3} => {Atr7=1} 0.4761905 1
## [5] {Atr13=3, Atr25=3} => {Atr7=1} 0.4761905 1
## [6] {Atr1=3, Atr25=3} => {Atr7=1} 0.4761905 1
## coverage lift count
## [1] 0.4761905 2.04878 40
## [2] 0.4761905 2.04878 40
## [3] 0.4761905 2.04878 40
## [4] 0.4761905 2.04878 40
## [5] 0.4761905 2.04878 40
## [6] 0.4761905 2.04878 40In the output for divorced individuals, some of the most meaningful association rules include: Here we see an interesting amout of rules proceeding to the question 7: We are like two strangers who share the same environment at home rather than family. In order to interpret those we should look at the distribution of answers inside the divorced group of individuals.
We can notice a distinctive shift in this plot compared to the one for the whole dataset which had 0 as the dominating answer. We can see that the answer of 1 is highly assosiated with the higer levels of answers to other questions. For example people that do not know their spouses well and do not find the time spend together special always answer 1 to the question about being strangers rather than family. It seems the shift in the dataset is logical. We can also observe a strong symetric assosiation rules between the 26 and 14 questions pretaining to having common goals and knowing your spouses concerns. Suggesting that if a person does not know their partners concerns they are also unlikely to having common goals.
bestrulesMconf <- sort(best_rules_married, by="support", decreasing = TRUE)
inspect(bestrulesMconf)## lhs rhs support confidence coverage lift count
## [1] {Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.4302326 0.9024390 0.4767442 1.583873 37
## [2] {Atr33=0,
## Atr35=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.4302326 0.9024390 0.4767442 1.583873 37
## [3] {Atr33=0,
## Atr36=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.4302326 0.9024390 0.4767442 1.583873 37
## [4] {Atr17=0,
## Atr33=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.4302326 0.9024390 0.4767442 1.583873 37
## [5] {Atr20=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.4069767 0.9210526 0.4418605 1.616541 35
## [6] {Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [7] {Atr12=0,
## Atr35=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [8] {Atr12=0,
## Atr20=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [9] {Atr12=0,
## Atr36=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [10] {Atr12=0,
## Atr20=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [11] {Atr12=0,
## Atr20=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [12] {Atr12=0,
## Atr17=0,
## Atr20=0,
## Atr33=0} => {Atr39=0} 0.3953488 0.9189189 0.4302326 1.612796 34
## [13] {Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3837209 0.9166667 0.4186047 1.642361 33
## [14] {Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [15] {Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [16] {Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3837209 0.9428571 0.4069767 1.654810 33
## [17] {Atr33=0,
## Atr34=0,
## Atr35=0,
## Atr38=0} => {Atr37=0} 0.3837209 0.9166667 0.4186047 1.642361 33
## [18] {Atr33=0,
## Atr34=0,
## Atr36=0,
## Atr38=0} => {Atr37=0} 0.3837209 0.9166667 0.4186047 1.642361 33
## [19] {Atr17=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3837209 0.9428571 0.4069767 1.654810 33
## [20] {Atr4=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [21] {Atr19=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [22] {Atr17=0,
## Atr33=0,
## Atr35=0,
## Atr37=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [23] {Atr17=0,
## Atr33=0,
## Atr36=0,
## Atr37=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [24] {Atr19=0,
## Atr33=0,
## Atr35=0,
## Atr37=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [25] {Atr19=0,
## Atr33=0,
## Atr36=0,
## Atr37=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [26] {Atr12=0,
## Atr33=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3837209 0.9705882 0.3953488 1.703481 33
## [27] {Atr12=0,
## Atr33=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3837209 0.9705882 0.3953488 1.703481 33
## [28] {Atr12=0,
## Atr20=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3837209 0.9428571 0.4069767 1.654810 33
## [29] {Atr12=0,
## Atr33=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3837209 0.9705882 0.3953488 1.703481 33
## [30] {Atr12=0,
## Atr19=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [31] {Atr7=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3837209 0.9166667 0.4186047 1.608844 33
## [32] {Atr15=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [33] {Atr6=0,
## Atr12=0,
## Atr15=0,
## Atr21=0} => {Atr13=0} 0.3720930 0.9142857 0.4069767 1.747302 32
## [34] {Atr6=0,
## Atr12=0,
## Atr16=0,
## Atr21=0} => {Atr13=0} 0.3720930 0.9142857 0.4069767 1.747302 32
## [35] {Atr5=0,
## Atr6=0,
## Atr12=0,
## Atr21=0} => {Atr13=0} 0.3720930 0.9142857 0.4069767 1.747302 32
## [36] {Atr33=0,
## Atr34=0,
## Atr38=0,
## Atr40=0} => {Atr37=0} 0.3720930 0.9142857 0.4069767 1.638095 32
## [37] {Atr22=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3720930 0.9142857 0.4069767 1.638095 32
## [38] {Atr9=0,
## Atr33=0,
## Atr37=0,
## Atr38=0} => {Atr34=0} 0.3720930 0.9142857 0.4069767 1.638095 32
## [39] {Atr9=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3720930 0.9142857 0.4069767 1.638095 32
## [40] {Atr7=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3720930 0.9142857 0.4069767 1.638095 32
## [41] {Atr19=0,
## Atr33=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [42] {Atr19=0,
## Atr20=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [43] {Atr15=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [44] {Atr15=0,
## Atr33=0,
## Atr35=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [45] {Atr15=0,
## Atr33=0,
## Atr36=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [46] {Atr17=0,
## Atr20=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [47] {Atr17=0,
## Atr22=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [48] {Atr7=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [49] {Atr19=0,
## Atr20=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9411765 0.3953488 1.651861 32
## [50] {Atr7=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [51] {Atr18=0,
## Atr20=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [52] {Atr12=0,
## Atr15=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [53] {Atr12=0,
## Atr15=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [54] {Atr12=0,
## Atr15=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [55] {Atr12=0,
## Atr19=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9411765 0.3953488 1.651861 32
## [56] {Atr7=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9411765 0.3953488 1.651861 32
## [57] {Atr12=0,
## Atr17=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [58] {Atr12=0,
## Atr16=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [59] {Atr12=0,
## Atr18=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [60] {Atr12=0,
## Atr17=0,
## Atr20=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [61] {Atr12=0,
## Atr16=0,
## Atr20=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [62] {Atr12=0,
## Atr18=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [63] {Atr12=0,
## Atr18=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [64] {Atr12=0,
## Atr17=0,
## Atr21=0,
## Atr33=0} => {Atr39=0} 0.3720930 0.9142857 0.4069767 1.604665 32
## [65] {Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3604651 0.9117647 0.3953488 1.633578 31
## [66] {Atr6=0,
## Atr11=0,
## Atr12=0,
## Atr21=0} => {Atr13=0} 0.3604651 0.9117647 0.3953488 1.742484 31
## [67] {Atr6=0,
## Atr12=0,
## Atr16=0,
## Atr30=0} => {Atr13=0} 0.3604651 0.9117647 0.3953488 1.742484 31
## [68] {Atr6=0,
## Atr12=0,
## Atr19=0,
## Atr21=0} => {Atr13=0} 0.3604651 0.9117647 0.3953488 1.742484 31
## [69] {Atr6=0,
## Atr12=0,
## Atr16=0,
## Atr28=0} => {Atr13=0} 0.3604651 0.9117647 0.3953488 1.742484 31
## [70] {Atr5=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3604651 0.9117647 0.3953488 1.633578 31
## [71] {Atr5=0,
## Atr34=0,
## Atr35=0,
## Atr38=0} => {Atr37=0} 0.3604651 0.9117647 0.3953488 1.633578 31
## [72] {Atr4=0,
## Atr9=0,
## Atr33=0,
## Atr37=0} => {Atr34=0} 0.3604651 0.9117647 0.3953488 1.633578 31
## [73] {Atr17=0,
## Atr37=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [74] {Atr15=0,
## Atr18=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [75] {Atr5=0,
## Atr15=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [76] {Atr15=0,
## Atr20=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [77] {Atr15=0,
## Atr22=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [78] {Atr7=0,
## Atr15=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [79] {Atr17=0,
## Atr18=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9393939 0.3837209 1.648732 31
## [80] {Atr5=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [81] {Atr4=0,
## Atr20=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [82] {Atr19=0,
## Atr22=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [83] {Atr10=0,
## Atr12=0,
## Atr20=0,
## Atr33=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [84] {Atr12=0,
## Atr15=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9393939 0.3837209 1.648732 31
## [85] {Atr12=0,
## Atr15=0,
## Atr16=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [86] {Atr12=0,
## Atr17=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9687500 0.3720930 1.700255 31
## [87] {Atr12=0,
## Atr21=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9687500 0.3720930 1.700255 31
## [88] {Atr12=0,
## Atr16=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9687500 0.3720930 1.700255 31
## [89] {Atr12=0,
## Atr18=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9393939 0.3837209 1.648732 31
## [90] {Atr12=0,
## Atr22=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9687500 0.3720930 1.700255 31
## [91] {Atr11=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [92] {Atr12=0,
## Atr21=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [93] {Atr4=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [94] {Atr5=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [95] {Atr12=0,
## Atr22=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [96] {Atr12=0,
## Atr20=0,
## Atr21=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [97] {Atr12=0,
## Atr16=0,
## Atr18=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [98] {Atr5=0,
## Atr12=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [99] {Atr5=0,
## Atr12=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [100] {Atr12=0,
## Atr20=0,
## Atr22=0,
## Atr38=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [101] {Atr12=0,
## Atr15=0,
## Atr21=0,
## Atr33=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [102] {Atr12=0,
## Atr15=0,
## Atr16=0,
## Atr33=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [103] {Atr12=0,
## Atr16=0,
## Atr17=0,
## Atr33=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [104] {Atr12=0,
## Atr19=0,
## Atr21=0,
## Atr33=0} => {Atr39=0} 0.3604651 0.9117647 0.3953488 1.600240 31
## [105] {Atr15=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [106] {Atr10=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [107] {Atr6=0,
## Atr12=0,
## Atr21=0,
## Atr29=0} => {Atr13=0} 0.3488372 0.9090909 0.3837209 1.737374 30
## [108] {Atr33=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [109] {Atr34=0,
## Atr35=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [110] {Atr22=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [111] {Atr9=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [112] {Atr34=0,
## Atr36=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [113] {Atr7=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [114] {Atr16=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [115] {Atr20=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [116] {Atr23=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3488372 0.9090909 0.3837209 1.628788 30
## [117] {Atr15=0,
## Atr33=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [118] {Atr15=0,
## Atr37=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [119] {Atr15=0,
## Atr35=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [120] {Atr15=0,
## Atr36=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [121] {Atr17=0,
## Atr33=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [122] {Atr17=0,
## Atr19=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [123] {Atr15=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [124] {Atr15=0,
## Atr16=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [125] {Atr30=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [126] {Atr17=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [127] {Atr17=0,
## Atr23=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [128] {Atr9=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [129] {Atr4=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [130] {Atr18=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [131] {Atr5=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [132] {Atr19=0,
## Atr23=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [133] {Atr10=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [134] {Atr10=0,
## Atr12=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [135] {Atr10=0,
## Atr12=0,
## Atr20=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [136] {Atr10=0,
## Atr12=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [137] {Atr10=0,
## Atr12=0,
## Atr21=0,
## Atr33=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [138] {Atr12=0,
## Atr15=0,
## Atr17=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [139] {Atr11=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [140] {Atr4=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [141] {Atr5=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [142] {Atr12=0,
## Atr23=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [143] {Atr9=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [144] {Atr12=0,
## Atr28=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [145] {Atr12=0,
## Atr23=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [146] {Atr9=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [147] {Atr12=0,
## Atr17=0,
## Atr18=0,
## Atr38=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [148] {Atr12=0,
## Atr30=0,
## Atr33=0,
## Atr40=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [149] {Atr12=0,
## Atr21=0,
## Atr30=0,
## Atr33=0} => {Atr39=0} 0.3488372 0.9375000 0.3720930 1.645408 30
## [150] {Atr12=0,
## Atr30=0,
## Atr33=0,
## Atr35=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [151] {Atr12=0,
## Atr30=0,
## Atr33=0,
## Atr36=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [152] {Atr12=0,
## Atr17=0,
## Atr28=0,
## Atr33=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [153] {Atr12=0,
## Atr16=0,
## Atr19=0,
## Atr33=0} => {Atr39=0} 0.3488372 0.9090909 0.3837209 1.595547 30
## [154] {Atr50=2} => {Atr51=2} 0.3372093 0.9354839 0.3604651 2.117148 29
## [155] {Atr7=0,
## Atr50=2} => {Atr51=2} 0.3372093 0.9354839 0.3604651 2.117148 29
## [156] {Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [157] {Atr6=0,
## Atr12=0,
## Atr17=0,
## Atr29=0} => {Atr13=0} 0.3372093 0.9062500 0.3720930 1.731944 29
## [158] {Atr6=0,
## Atr8=0,
## Atr12=0,
## Atr21=0} => {Atr13=0} 0.3372093 0.9062500 0.3720930 1.731944 29
## [159] {Atr6=0,
## Atr12=0,
## Atr16=0,
## Atr29=0} => {Atr13=0} 0.3372093 0.9354839 0.3604651 1.787814 29
## [160] {Atr5=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [161] {Atr20=0,
## Atr34=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [162] {Atr20=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [163] {Atr4=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [164] {Atr19=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [165] {Atr8=0,
## Atr33=0,
## Atr37=0,
## Atr38=0} => {Atr34=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [166] {Atr8=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [167] {Atr18=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [168] {Atr28=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [169] {Atr9=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr34=0} 0.3372093 0.9062500 0.3720930 1.623698 29
## [170] {Atr15=0,
## Atr16=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [171] {Atr15=0,
## Atr19=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [172] {Atr15=0,
## Atr18=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [173] {Atr5=0,
## Atr15=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [174] {Atr15=0,
## Atr20=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [175] {Atr15=0,
## Atr22=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [176] {Atr7=0,
## Atr15=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [177] {Atr11=0,
## Atr19=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [178] {Atr17=0,
## Atr18=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [179] {Atr24=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [180] {Atr24=0,
## Atr33=0,
## Atr35=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [181] {Atr23=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [182] {Atr24=0,
## Atr33=0,
## Atr36=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [183] {Atr15=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [184] {Atr15=0,
## Atr23=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [185] {Atr9=0,
## Atr15=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [186] {Atr17=0,
## Atr21=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [187] {Atr16=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [188] {Atr4=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [189] {Atr17=0,
## Atr28=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [190] {Atr19=0,
## Atr21=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [191] {Atr16=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [192] {Atr4=0,
## Atr18=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [193] {Atr19=0,
## Atr28=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [194] {Atr9=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [195] {Atr19=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [196] {Atr17=0,
## Atr33=0,
## Atr40=0,
## Atr41=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [197] {Atr10=0,
## Atr12=0,
## Atr15=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [198] {Atr10=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9666667 0.3488372 1.696599 29
## [199] {Atr10=0,
## Atr11=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [200] {Atr10=0,
## Atr12=0,
## Atr16=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [201] {Atr10=0,
## Atr12=0,
## Atr19=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [202] {Atr10=0,
## Atr12=0,
## Atr18=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [203] {Atr7=0,
## Atr10=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [204] {Atr12=0,
## Atr15=0,
## Atr21=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [205] {Atr12=0,
## Atr15=0,
## Atr22=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [206] {Atr12=0,
## Atr28=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [207] {Atr5=0,
## Atr12=0,
## Atr17=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [208] {Atr12=0,
## Atr18=0,
## Atr21=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [209] {Atr5=0,
## Atr12=0,
## Atr16=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [210] {Atr12=0,
## Atr18=0,
## Atr22=0,
## Atr38=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [211] {Atr12=0,
## Atr26=0,
## Atr33=0,
## Atr40=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [212] {Atr12=0,
## Atr26=0,
## Atr33=0,
## Atr35=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [213] {Atr12=0,
## Atr26=0,
## Atr33=0,
## Atr36=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [214] {Atr12=0,
## Atr17=0,
## Atr30=0,
## Atr33=0} => {Atr39=0} 0.3372093 0.9354839 0.3604651 1.641870 29
## [215] {Atr15=0,
## Atr25=0,
## Atr33=0,
## Atr40=0} => {Atr39=0} 0.3372093 0.9062500 0.3720930 1.590561 29
## [216] {Atr29=0,
## Atr50=2} => {Atr51=2} 0.3255814 0.9333333 0.3488372 2.112281 28
## [217] {Atr36=0,
## Atr50=2} => {Atr51=2} 0.3255814 0.9333333 0.3488372 2.112281 28
## [218] {Atr7=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3255814 0.9333333 0.3488372 2.112281 28
## [219] {Atr7=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3255814 0.9333333 0.3488372 2.112281 28
## [220] {Atr34=0,
## Atr38=0,
## Atr39=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [221] {Atr17=0,
## Atr34=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [222] {Atr4=0,
## Atr34=0,
## Atr39=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [223] {Atr19=0,
## Atr34=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [224] {Atr12=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9655172 0.3372093 1.694581 28
## [225] {Atr6=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [226] {Atr1=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [227] {Atr1=0,
## Atr6=0,
## Atr12=0,
## Atr21=0} => {Atr13=0} 0.3255814 0.9032258 0.3604651 1.726165 28
## [228] {Atr6=0,
## Atr11=0,
## Atr12=0,
## Atr29=0} => {Atr13=0} 0.3255814 0.9032258 0.3604651 1.726165 28
## [229] {Atr33=0,
## Atr34=0,
## Atr38=0,
## Atr39=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [230] {Atr34=0,
## Atr38=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [231] {Atr34=0,
## Atr35=0,
## Atr38=0,
## Atr39=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [232] {Atr34=0,
## Atr36=0,
## Atr38=0,
## Atr39=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [233] {Atr17=0,
## Atr34=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [234] {Atr17=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [235] {Atr4=0,
## Atr34=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [236] {Atr4=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [237] {Atr19=0,
## Atr34=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [238] {Atr19=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [239] {Atr18=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [240] {Atr23=0,
## Atr34=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [241] {Atr4=0,
## Atr9=0,
## Atr34=0,
## Atr39=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [242] {Atr9=0,
## Atr10=0,
## Atr33=0,
## Atr37=0} => {Atr34=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [243] {Atr15=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [244] {Atr11=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [245] {Atr17=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [246] {Atr4=0,
## Atr5=0,
## Atr34=0,
## Atr38=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [247] {Atr9=0,
## Atr30=0,
## Atr33=0,
## Atr37=0} => {Atr34=0} 0.3255814 0.9333333 0.3488372 1.672222 28
## [248] {Atr12=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9655172 0.3372093 1.694581 28
## [249] {Atr12=0,
## Atr33=0,
## Atr35=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9655172 0.3372093 1.694581 28
## [250] {Atr12=0,
## Atr20=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9655172 0.3372093 1.694581 28
## [251] {Atr12=0,
## Atr33=0,
## Atr36=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9655172 0.3372093 1.694581 28
## [252] {Atr15=0,
## Atr17=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [253] {Atr6=0,
## Atr7=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3255814 0.9032258 0.3604651 1.618280 28
## [254] {Atr18=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [255] {Atr20=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [256] {Atr22=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [257] {Atr7=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [258] {Atr11=0,
## Atr15=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [259] {Atr4=0,
## Atr15=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [260] {Atr15=0,
## Atr28=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [261] {Atr11=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [262] {Atr15=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [263] {Atr17=0,
## Atr33=0,
## Atr34=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [264] {Atr17=0,
## Atr34=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [265] {Atr3=0,
## Atr33=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [266] {Atr15=0,
## Atr17=0,
## Atr33=0,
## Atr41=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [267] {Atr10=0,
## Atr12=0,
## Atr17=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [268] {Atr10=0,
## Atr12=0,
## Atr21=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [269] {Atr4=0,
## Atr10=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [270] {Atr5=0,
## Atr10=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [271] {Atr10=0,
## Atr12=0,
## Atr16=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [272] {Atr10=0,
## Atr12=0,
## Atr28=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [273] {Atr10=0,
## Atr21=0,
## Atr30=0,
## Atr39=0} => {Atr12=0} 0.3255814 1.0000000 0.3255814 1.535714 28
## [274] {Atr1=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [275] {Atr1=0,
## Atr4=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [276] {Atr1=0,
## Atr12=0,
## Atr19=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [277] {Atr1=0,
## Atr12=0,
## Atr35=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [278] {Atr1=0,
## Atr12=0,
## Atr20=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [279] {Atr1=0,
## Atr12=0,
## Atr36=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [280] {Atr8=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [281] {Atr12=0,
## Atr27=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [282] {Atr8=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [283] {Atr12=0,
## Atr29=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [284] {Atr5=0,
## Atr12=0,
## Atr21=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [285] {Atr5=0,
## Atr12=0,
## Atr22=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [286] {Atr12=0,
## Atr15=0,
## Atr30=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [287] {Atr12=0,
## Atr22=0,
## Atr26=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [288] {Atr12=0,
## Atr16=0,
## Atr30=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9333333 0.3488372 1.638095 28
## [289] {Atr12=0,
## Atr22=0,
## Atr30=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [290] {Atr12=0,
## Atr17=0,
## Atr27=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [291] {Atr12=0,
## Atr17=0,
## Atr29=0,
## Atr33=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [292] {Atr25=0,
## Atr33=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [293] {Atr17=0,
## Atr24=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3255814 0.9032258 0.3604651 1.585253 28
## [294] {Atr8=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [295] {Atr35=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9642857 0.3255814 2.182331 27
## [296] {Atr23=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [297] {Atr9=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [298] {Atr8=0,
## Atr9=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [299] {Atr7=0,
## Atr8=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [300] {Atr29=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [301] {Atr35=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9642857 0.3255814 2.182331 27
## [302] {Atr7=0,
## Atr35=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9642857 0.3255814 2.182331 27
## [303] {Atr7=0,
## Atr23=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [304] {Atr7=0,
## Atr9=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [305] {Atr9=0,
## Atr32=0,
## Atr37=0} => {Atr34=0} 0.3139535 0.9310345 0.3372093 1.668103 27
## [306] {Atr7=0,
## Atr8=0,
## Atr9=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [307] {Atr7=0,
## Atr29=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9310345 0.3372093 2.107078 27
## [308] {Atr7=0,
## Atr35=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3139535 0.9642857 0.3255814 2.182331 27
## [309] {Atr9=0,
## Atr32=0,
## Atr33=0,
## Atr37=0} => {Atr34=0} 0.3139535 0.9642857 0.3255814 1.727679 27
## [310] {Atr9=0,
## Atr32=0,
## Atr35=0,
## Atr37=0} => {Atr34=0} 0.3139535 0.9310345 0.3372093 1.668103 27
## [311] {Atr9=0,
## Atr22=0,
## Atr32=0,
## Atr37=0} => {Atr34=0} 0.3139535 0.9310345 0.3372093 1.668103 27
## [312] {Atr9=0,
## Atr32=0,
## Atr36=0,
## Atr37=0} => {Atr34=0} 0.3139535 0.9310345 0.3372093 1.668103 27
## [313] {Atr19=0,
## Atr20=0,
## Atr34=0,
## Atr37=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [314] {Atr9=0,
## Atr33=0,
## Atr37=0,
## Atr41=0} => {Atr34=0} 0.3139535 0.9310345 0.3372093 1.668103 27
## [315] {Atr12=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3139535 0.9642857 0.3255814 1.692420 27
## [316] {Atr12=0,
## Atr22=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3139535 0.9642857 0.3255814 1.692420 27
## [317] {Atr7=0,
## Atr12=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3139535 0.9642857 0.3255814 1.692420 27
## [318] {Atr4=0,
## Atr15=0,
## Atr37=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [319] {Atr6=0,
## Atr22=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3139535 0.9310345 0.3372093 1.668103 27
## [320] {Atr1=0,
## Atr10=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [321] {Atr10=0,
## Atr12=0,
## Atr28=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [322] {Atr10=0,
## Atr12=0,
## Atr22=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [323] {Atr9=0,
## Atr10=0,
## Atr12=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [324] {Atr10=0,
## Atr12=0,
## Atr30=0,
## Atr33=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [325] {Atr1=0,
## Atr12=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9642857 0.3255814 1.692420 27
## [326] {Atr12=0,
## Atr30=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [327] {Atr12=0,
## Atr27=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [328] {Atr12=0,
## Atr29=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [329] {Atr12=0,
## Atr26=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [330] {Atr12=0,
## Atr17=0,
## Atr26=0,
## Atr33=0} => {Atr39=0} 0.3139535 0.9310345 0.3372093 1.634061 27
## [331] {Atr27=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [332] {Atr19=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [333] {Atr28=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [334] {Atr20=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [335] {Atr27=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [336] {Atr7=0,
## Atr27=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [337] {Atr7=0,
## Atr19=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [338] {Atr8=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [339] {Atr8=0,
## Atr23=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [340] {Atr8=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [341] {Atr28=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [342] {Atr29=0,
## Atr35=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9629630 0.3139535 2.179337 26
## [343] {Atr20=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [344] {Atr23=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [345] {Atr9=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [346] {Atr7=0,
## Atr28=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [347] {Atr7=0,
## Atr20=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [348] {Atr9=0,
## Atr23=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [349] {Atr23=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [350] {Atr9=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [351] {Atr2=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [352] {Atr12=0,
## Atr38=0,
## Atr41=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [353] {Atr7=0,
## Atr27=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [354] {Atr8=0,
## Atr9=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [355] {Atr7=0,
## Atr8=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [356] {Atr8=0,
## Atr9=0,
## Atr23=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [357] {Atr7=0,
## Atr8=0,
## Atr23=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [358] {Atr8=0,
## Atr9=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [359] {Atr7=0,
## Atr8=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [360] {Atr7=0,
## Atr28=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [361] {Atr29=0,
## Atr35=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9629630 0.3139535 2.179337 26
## [362] {Atr7=0,
## Atr29=0,
## Atr35=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9629630 0.3139535 2.179337 26
## [363] {Atr7=0,
## Atr20=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [364] {Atr7=0,
## Atr23=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [365] {Atr7=0,
## Atr9=0,
## Atr29=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [366] {Atr7=0,
## Atr9=0,
## Atr23=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [367] {Atr7=0,
## Atr23=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [368] {Atr7=0,
## Atr9=0,
## Atr36=0,
## Atr50=2} => {Atr51=2} 0.3023256 0.9285714 0.3255814 2.101504 26
## [369] {Atr9=0,
## Atr32=0,
## Atr37=0,
## Atr40=0} => {Atr34=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [370] {Atr5=0,
## Atr9=0,
## Atr32=0,
## Atr37=0} => {Atr34=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [371] {Atr9=0,
## Atr20=0,
## Atr32=0,
## Atr37=0} => {Atr34=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [372] {Atr7=0,
## Atr9=0,
## Atr32=0,
## Atr37=0} => {Atr34=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [373] {Atr17=0,
## Atr19=0,
## Atr34=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [374] {Atr17=0,
## Atr18=0,
## Atr34=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [375] {Atr9=0,
## Atr37=0,
## Atr38=0,
## Atr41=0} => {Atr34=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [376] {Atr9=0,
## Atr30=0,
## Atr37=0,
## Atr38=0} => {Atr34=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [377] {Atr12=0,
## Atr21=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [378] {Atr12=0,
## Atr19=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [379] {Atr12=0,
## Atr18=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [380] {Atr5=0,
## Atr12=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [381] {Atr12=0,
## Atr23=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [382] {Atr2=0,
## Atr33=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [383] {Atr2=0,
## Atr33=0,
## Atr35=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [384] {Atr2=0,
## Atr33=0,
## Atr36=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [385] {Atr2=0,
## Atr17=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [386] {Atr2=0,
## Atr20=0,
## Atr37=0,
## Atr40=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [387] {Atr6=0,
## Atr19=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [388] {Atr6=0,
## Atr23=0,
## Atr39=0,
## Atr40=0} => {Atr37=0} 0.3023256 0.9285714 0.3255814 1.663690 26
## [389] {Atr1=0,
## Atr17=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [390] {Atr15=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [391] {Atr17=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [392] {Atr4=0,
## Atr24=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [393] {Atr19=0,
## Atr30=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [394] {Atr17=0,
## Atr27=0,
## Atr33=0,
## Atr37=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [395] {Atr12=0,
## Atr17=0,
## Atr20=0,
## Atr34=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [396] {Atr3=0,
## Atr15=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [397] {Atr12=0,
## Atr38=0,
## Atr40=0,
## Atr41=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [398] {Atr12=0,
## Atr19=0,
## Atr38=0,
## Atr41=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [399] {Atr12=0,
## Atr35=0,
## Atr38=0,
## Atr41=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [400] {Atr12=0,
## Atr20=0,
## Atr38=0,
## Atr41=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [401] {Atr12=0,
## Atr36=0,
## Atr38=0,
## Atr41=0} => {Atr39=0} 0.3023256 0.9629630 0.3139535 1.690098 26
## [402] {Atr2=0,
## Atr12=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [403] {Atr2=0,
## Atr12=0,
## Atr17=0,
## Atr33=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [404] {Atr2=0,
## Atr12=0,
## Atr21=0,
## Atr33=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [405] {Atr10=0,
## Atr12=0,
## Atr23=0,
## Atr38=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [406] {Atr12=0,
## Atr24=0,
## Atr38=0,
## Atr40=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [407] {Atr12=0,
## Atr26=0,
## Atr33=0,
## Atr38=0} => {Atr39=0} 0.3023256 0.9285714 0.3255814 1.629738 26
## [408] {Atr3=0,
## Atr10=0,
## Atr21=0,
## Atr40=0} => {Atr12=0} 0.3023256 1.0000000 0.3023256 1.535714 26For married individuals, some of the top meaningful association rules are: Similarly to the the previous set we have a question that has a high distribiution of answer 0 inside the group of married individuals dominating the best rules - 39. Fights often occur suddenly.
As before while looking on the distribution of answers we see a shift and a left side skewness. Which is rational as we previously could see that a sudden fights are associated with the divorced status of marriage. Essentially, it indicates a pattern where people who avoid certain conflict-related behaviors are likely to not experience sudden fights in the relationship as well.
These association rules highlight specific patterns and connections between answers to different questions, providing valuable insights into the factors that may contribute to marital outcomes for both divorced and married individuals.
Conclusions
Firstly we did the analysis of association rules with the consequent as divorced individuals provides insights into specific patterns and behaviors associated with the likelihood of divorce. Then in contrast, examining association rules with the consequent as married individuals offers a distinct perspective, shedding light on characteristics and behaviors that contribute to marital stability. In the next step we examine association rules inside the subsets of married and divorced individuals to gain more knowlage about the behaviour of people with specific marital status. The separation into married and divorced subsets allowed us to explore associations between responses to specific questions within each group. This nuanced approach unveils patterns and unique connections unique t, providing valuable insights into the dynamics that contribute to marital success and challenges. Analyzing associations within these subsets enables a targeted understanding of the factors influencing individuals within each group, contributing to a more tailored and insightful interpretation of the data.
References:
Yöntem, Mustafa & Adem, Kemal & Ilhan, Tahsin & Kılıçarslan, Serhat. (2019). DIVORCE PREDICTION USING CORRELATION BASED FEATURE SELECTION AND ARTIFICIAL NEURAL NETWORKS https://www.researchgate.net/publication/334170931_DIVORCE_PREDICTION_USING_CORRELATION_BASED_FEATURE_SELECTION_AND_ARTIFICIAL_NEURAL_NETWORKS
Yöntem, M. K., Adem, K., İlhan, T., and Kılıçarslan, S. (2018). Çok Katmanlı Algılayıcı Sinir Ağı ve C4. 5 Karar Ağacı Algoritmaları ile Boşanma Tahmini. 271 International Congress on Politic, Economic and Social Studies (ICPESS).