2
$\begingroup$

I'm studying occurence of Behavior11, Behavior12,Behavior2,Behavior3 according three variables :

Times : task time

Time_interval :task time in interval

Frequency:Frequency of the task

For this purpose, I use GLM

attach(datas)
an11=anova(glm(Behavior11 ~  Times + Frequency    , family=binomial),test="Chisq")
an12=anova(glm(Behavior12 ~  Times_interval+ Frequency   , family=binomial),test="Chisq")
an3=anova(glm(Behavior3 ~  Times_interval+ Frequency   , family=binomial),test="Chisq")
an2=anova(glm(Behavior2 ~  Times_interval+ Frequency   , family=binomial),test="Chisq")

I have different significant effect for every behavior. Odds value reveals the direction of dependence exemple:

model1=glm(Behavior12 ~  Times_interval+ Frequency, family=binomial)
summary(model1)
exp(model1$coefficients)

Coefficients:
                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)           -2.84731    0.53984  -5.274 1.33e-07 ***
Times_interval(10,20]  0.20841    0.37449   0.557   0.5778    
Times_interval(20,30]  0.65672    0.40334   1.628   0.1035    
Times_interval(30,40]  0.49951    0.60114   0.831   0.4060    
Times_interval(40,50] -0.18637    0.83938  -0.222   0.8243    
Times_interval(50,60]  1.16718    0.70834   1.648   0.0994 .  
Frequency              0.02714    0.01380   1.967   0.0492 *  


exp(model1$coefficients)
 Frequency 
 1.02750856

As frequency grows Behavior12 grows too at a given rate.

Now, my aim is to have something like equation predicting occurence of behavior. My input data are Times , Time_intervaland Frequency. We will have always the same percentage of each Frequencynumber and Times too, exactly like the dataset

My output should generate a behavior. If I execute n=1000 times the 'equation'. The ouput would be the same percentage of behavior than in the dataset.

How to obtain probalities values of behavior in link with input data, and to formalize them in one equation ( formula) ?

Thanks a lot

    datas=structure(list(Behavior2 = c(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 
0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 
0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0), Behavior3 = c(1, 1, 1, 1, 1, 1, 1, 0, 1, 
0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 
0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 
1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 
1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 
1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 
1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 
0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 
1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 
1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 
0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 
0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 
1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 
1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 
1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 
0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 
1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 
0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 
1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 1, 0, 0, 0, 0), Behavior12 = c(0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 
0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 
0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0), Behavior11 = c(0, 0, 
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 
0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 
0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 
1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0), Frequency = c(11L, 
11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 11L, 11L, 11L, 
11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 9L, 9L, 12L, 12L, 12L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 31L, 31L, 31L, 31L, 
31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 
31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 
31L, 31L, 31L, 31L, 31L, 31L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 6L, 
6L, 6L, 9L, 9L, 9L, 9L, 9L, 9L, 36L, 36L, 36L, 36L, 36L, 36L, 
36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 
36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 
36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 
36L, 36L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 1L, 21L, 21L, 21L, 21L, 
21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
21L, 21L, 21L, 21L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
11L, 11L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 5L, 5L, 5L, 5L, 18L, 18L, 
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
18L, 18L, 18L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 
42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 
42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 
42L, 42L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
12L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
18L, 18L, 18L, 11L, 11L, 11L, 11L, 11L, 11L, 9L, 9L, 9L, 12L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 6L, 6L, 6L, 6L, 6L, 6L, 
11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
11L, 11L, 11L, 11L, 11L, 9L, 11L, 11L, 6L, 6L, 6L, 6L, 6L, 12L, 
12L, 12L, 12L, 12L, 12L, 12L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 
25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 
25L, 25L, 25L, 25L, 25L, 3L, 3L, 3L, 18L, 18L, 18L, 18L, 18L, 
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L), Times = c(15, 15, 15, 15, 15, 15, 15, 15, 
15, 15, 15, 15, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 
17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 47, 47, 33, 33, 33, 
33, 33, 33, 33, 33, 33, 33, 33, 33, 28, 28, 28, 28, 28, 28, 28, 
28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 
28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 43, 44, 44, 
44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 39, 
29, 29, 29, 32, 32, 32, 32, 32, 32, 9, 9, 9, 9, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 58, 58, 58, 
58, 58, 58, 58, 38, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 
20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 51, 51, 51, 51, 51, 51, 
51, 51, 51, 51, 51, 43, 43, 43, 43, 43, 43, 28, 28, 28, 28, 28, 
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 14, 14, 14, 14, 14, 14, 14, 14, 
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 33, 33, 
33, 33, 33, 36, 36, 36, 36, 36, 36, 36, 9, 9, 9, 9, 9, 9, 9, 
9, 9, 9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 35, 35, 35, 30, 
30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 
30, 30, 30, 30, 30, 37, 37, 37, 32, 32, 32, 18, 18, 18, 18, 18, 
18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 30, 22, 22, 
25, 25, 25, 25, 25, 50, 50, 50, 50, 50, 50, 50, 26, 26, 26, 26, 
26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 
26, 26, 26, 26, 26, 26, 26, 26, 26, 23, 23, 23, 23, 23, 23, 23, 
23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 
23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 
23, 23, 23, 23, 23, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 
17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 
17, 17, 17, 52, 52, 52, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 
11, 11, 11, 11, 11, 11, 11, 11, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6), Times_interval = structure(c(2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 4L, 4L, 4L, 4L, 4L, 
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3L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
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3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
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2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("(0,10]", 
"(10,20]", "(20,30]", "(30,40]", "(40,50]", "(50,60]"), class = "factor")), .Names = c("Behavior2", 
"Behavior3", "Behavior12", "Behavior11", "Frequency", "Times", 
"Times_interval"), class = "data.frame", row.names = c(1L, 2L, 
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43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 
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69L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 
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315L, 316L, 317L, 318L, 319L, 320L, 321L, 322L, 323L, 324L, 325L, 
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536L, 537L, 538L, 539L, 540L, 541L, 542L, 543L, 544L, 545L))
$\endgroup$
  • $\begingroup$ Welcome to DataScience! I'm sorry, I don't really understand your question. Are you looking to get the probability of each behaviour according to your model? Since this is very stats-related, it might be better suited to CrossValidated. $\endgroup$ – StatsSorceress Dec 8 '18 at 17:38
  • $\begingroup$ Thanks! yes I'm looking to get the probability of each behaviour according to the models, but the probability by taking into account the proba of the other. The aim is to simulate and generate through one and same relationship every time one behavior according to entries parameter. So in the final i run the equation 1000 time i will have for example 60% of behavior3, and 20% of behavior11... $\endgroup$ – ranell Dec 12 '18 at 8:13
1
+50
$\begingroup$

I would extract the beta coefficients (ß) from the model and insert them into the formula for calculating the probability (p) as described on Wikipedia p = exp(ß_0 + ß_1*x_1 + … + ß_n*x_n) / (1 + exp(ß_0 + ß_1*x_1 + … + ß_n*x_n)). This formula is applied when you predict from the logistic regression model in R Setting type = "response". In many regression models in R ß_0 is called Intercept and you can remove it from your model calculation by appending - 1 to your formula. You can also do transformations for example by using the log() function in your formula. Here is some examplary R-code mostly for what I previously described:

#inspect the data for Times, log(Frequency) and Behavior11
if(!("ggplot2" %in% installed.packages()[,"Package"])) install.packages("ggplot2");
require(ggplot2);
ggplot(
  data = datas
  ,aes(x = Times
       ,y = log(Frequency)
       ,color = factor(Behavior11))) +
geom_point() + 
theme_bw();

#calculate logistic regression model for Behavior11
glm_B11 <- glm(
  data = datas
  ,Behavior11 ~ Times + log(Frequency) - 1
  ,family = binomial);

#see using log(Frequency) and removing the Intercept
#results in highly significant test-values
summary(glm_B11);

#extract the beta values from the model
(beta_Times <- as.numeric(glm_B11$coefficients["Times"]));
(beta_logFrequency <- as.numeric(glm_B11$coefficients["log(Frequency)"]));

#this is the formula to calculate (the probability of) Behavior11
B11_predicted_from_formula <- exp(beta_Times*datas$Times + beta_logFrequency*log(datas$Frequency)) /
   (1 + exp(beta_Times*datas$Times + beta_logFrequency*log(datas$Frequency));

#the prediction of (the probability of) Behavior11 gives the same result
B11_predicted_from_model <- predict(
  glm_B11
  ,data = datas
  ,type = "response");
sum(B11_predicted_from_formula - B11_predicted_from_model);
$\endgroup$
  • $\begingroup$ Thanks a lot. this is a formula for one behavior. Is there any way to model in one glm in order to extract beta value and have function that generate each execution one behavior. Because there is relationship. If frequency is more important i have more chance to have Behavior11 than Behavior3 for example.. leglm( data = datas ,Behavior11 + Behavior12 + Behavior3+ Behavior2 ~ Times + log(Frequency) - 1 ,family = binomial); $\endgroup$ – ranell Dec 11 '18 at 20:14
  • $\begingroup$ You could check association rule mining. It's an unsupervised learning technique for exploring associations like e.g. between different behaviors. rdatamining.com/examples/association-rules $\endgroup$ – Franziska W. Dec 17 '18 at 18:27

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