Project 1: Logistic Regression

Descriptive Analysis

Overall

## 
##  Descriptive statistics by group 
## group: 0
##             vars    n  mean    sd median trimmed   mad min max range  skew
## Q211*          1 1013  1.00  0.00      1    1.00  0.00   1   1     0   NaN
## intinpol*      2 1013  2.75  0.86      3    2.77  1.48   1   4     3 -0.10
## townsize*      3 1013  3.31  1.51      4    3.38  1.48   1   5     4 -0.32
## settlement*    4 1013  3.16  1.27      3    3.14  1.48   1   5     4  0.33
## region*        5 1013  4.25  2.29      4    4.19  2.97   1   8     7  0.26
## age            6 1013 45.34 17.20     43   44.46 19.27  18  91    73  0.38
## income1        7 1013  3.80  1.93      4    3.77  1.48   0   9     9  0.13
## eduT*          8 1013  1.31  0.46      1    1.26  0.00   1   2     1  0.83
##             kurtosis   se
## Q211*            NaN 0.00
## intinpol*      -0.77 0.03
## townsize*      -1.35 0.05
## settlement*    -1.13 0.04
## region*        -1.22 0.07
## age            -0.82 0.54
## income1        -0.37 0.06
## eduT*          -1.32 0.01
## ------------------------------------------------------------ 
## group: 1
##             vars   n  mean    sd median trimmed   mad min max range  skew
## Q211*          1 723  2.00  0.00      2    2.00  0.00   2   2     0   NaN
## intinpol*      2 723  2.50  0.82      3    2.50  1.48   1   4     3 -0.02
## townsize*      3 723  3.30  1.59      4    3.37  1.48   1   5     4 -0.34
## settlement*    4 723  3.00  1.40      3    3.00  1.48   1   5     4  0.32
## region*        5 723  3.85  2.19      4    3.72  2.97   1   8     7  0.53
## age            6 723 45.93 16.86     45   45.30 19.27  18  90    72  0.26
## income1        7 723  3.73  1.94      4    3.72  1.48   0   9     9  0.07
## eduT*          8 723  1.36  0.48      1    1.32  0.00   1   2     1  0.58
##             kurtosis   se
## Q211*            NaN 0.00
## intinpol*      -0.54 0.03
## townsize*      -1.44 0.06
## settlement*    -1.22 0.05
## region*        -1.01 0.08
## age            -0.85 0.63
## income1        -0.45 0.07
## eduT*          -1.66 0.02

Overall, our variable of interest - attending lawful demonstations (Q211) - has two levels. There are 723 citizens who would attend such demonstations and 1013 of those who would not.

• The group which would attend lawful demonstrations is characterized by higher, in average, interest in politics, compared with those who would not attend lawful demonstrations
• While considering other variables, there is no obvious differences between groups.

Outcome variable + predictors

• Interest in politics

Interesting to notice that in most cases people who would attend lawful demonstration has higher median age than those, who would not.

• settlement

The biggest share of citizens who would attend lawful demonstrations live in regional centers, district centers or villages.

• edu+income

Those who would attend lawful demonstrations are characterized by Fifth step of income, no matter which education they gained.

Model building

## 
## Call:
## glm(formula = Q211 ~ intinpol + settlement + eduT + income1 + 
##     age + region, family = "binomial", data = df2)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.8052  -1.0272  -0.7765   1.2232   2.0811  
## 
## Coefficients:
##                                                                    Estimate
## (Intercept)                                                       0.9960171
## intinpolSomewhat interested                                      -0.4609568
## intinpolNot very interested                                      -0.6365091
## intinpolNot at all interested                                    -1.4088843
## settlementRegional center                                        -0.4597112
## settlementDistrict center                                        -0.8721639
## settlementAnother city, town (not a regional or district center) -0.9810863
## settlementVillage                                                -0.5133248
## eduT1                                                             0.1788241
## income1                                                          -0.0544330
## age                                                              -0.0009979
## regionRU: Central Federal District                                0.3000963
## regionRU: North Caucasian federal district                       -0.0151321
## regionRU: Volga; Privolzhsky Federal District                     0.1584737
## regionRU: Urals Federal District                                 -0.2816908
## regionRU: Far East Federal District                              -0.1589217
## regionRU: Siberian Federal District                               0.2246221
## regionRU: South Federal District                                 -0.4919488
##                                                                  Std. Error
## (Intercept)                                                       0.3734018
## intinpolSomewhat interested                                       0.1937967
## intinpolNot very interested                                       0.1931379
## intinpolNot at all interested                                     0.2251833
## settlementRegional center                                         0.2254509
## settlementDistrict center                                         0.2170352
## settlementAnother city, town (not a regional or district center)  0.3581382
## settlementVillage                                                 0.2284048
## eduT1                                                             0.1138132
## income1                                                           0.0289287
## age                                                               0.0031580
## regionRU: Central Federal District                                0.2042000
## regionRU: North Caucasian federal district                        0.2849057
## regionRU: Volga; Privolzhsky Federal District                     0.2011626
## regionRU: Urals Federal District                                  0.2401377
## regionRU: Far East Federal District                               0.2952891
## regionRU: Siberian Federal District                               0.2140290
## regionRU: South Federal District                                  0.2419097
##                                                                  z value
## (Intercept)                                                        2.667
## intinpolSomewhat interested                                       -2.379
## intinpolNot very interested                                       -3.296
## intinpolNot at all interested                                     -6.257
## settlementRegional center                                         -2.039
## settlementDistrict center                                         -4.019
## settlementAnother city, town (not a regional or district center)  -2.739
## settlementVillage                                                 -2.247
## eduT1                                                              1.571
## income1                                                           -1.882
## age                                                               -0.316
## regionRU: Central Federal District                                 1.470
## regionRU: North Caucasian federal district                        -0.053
## regionRU: Volga; Privolzhsky Federal District                      0.788
## regionRU: Urals Federal District                                  -1.173
## regionRU: Far East Federal District                               -0.538
## regionRU: Siberian Federal District                                1.049
## regionRU: South Federal District                                  -2.034
##                                                                  Pr(>|z|)    
## (Intercept)                                                      0.007644 ** 
## intinpolSomewhat interested                                      0.017381 *  
## intinpolNot very interested                                      0.000982 ***
## intinpolNot at all interested                                    3.93e-10 ***
## settlementRegional center                                        0.041443 *  
## settlementDistrict center                                        5.86e-05 ***
## settlementAnother city, town (not a regional or district center) 0.006155 ** 
## settlementVillage                                                0.024612 *  
## eduT1                                                            0.116135    
## income1                                                          0.059886 .  
## age                                                              0.752001    
## regionRU: Central Federal District                               0.141665    
## regionRU: North Caucasian federal district                       0.957642    
## regionRU: Volga; Privolzhsky Federal District                    0.430820    
## regionRU: Urals Federal District                                 0.240780    
## regionRU: Far East Federal District                              0.590446    
## regionRU: Siberian Federal District                              0.293951    
## regionRU: South Federal District                                 0.041991 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2357.9  on 1735  degrees of freedom
## Residual deviance: 2247.4  on 1718  degrees of freedom
## AIC: 2283.4
## 
## Number of Fisher Scoring iterations: 4

The Null-Hypothesis will be: the given variable does not have an influence on the attending lawful demonstrations The Alternative Hypothesis will be: the given variable does have an influence on attending lawful demonstrations.

Lets pay some attention on variables which P-value is less than 0.05. The probability of finding the result like this or more extreme, assuming that such variables as intinpol, settlement, region have no effect is less than 5%. Therefore, we reject the Null-Hypothesis and assume that these variables do have a significant influence on attending lawful demonstrations.

Next, we have a look at variables which P-value is more than 0.05. The probability of finding the result like this or more extreme, assuming that such variables as age, eduT, income1 have no effect is more than 5%. Therefore, we accept the Null-Hypothesis and assume that these variables do not have a significant influence on attending lawful demonstrations.

Model Specification

Next, we want to figure out which variables to include in final model and drop out insignificant ones in order to get rid of the noise they can produce.

## 
## Call:
## glm(formula = Q211 ~ intinpol + settlement + eduT + income1 + 
##     region, family = "binomial", data = df2)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.8079  -1.0261  -0.7772   1.2216   2.0782  
## 
## Coefficients:
##                                                                  Estimate
## (Intercept)                                                       0.93837
## intinpolSomewhat interested                                      -0.45765
## intinpolNot very interested                                      -0.63021
## intinpolNot at all interested                                    -1.39997
## settlementRegional center                                        -0.45944
## settlementDistrict center                                        -0.87407
## settlementAnother city, town (not a regional or district center) -0.97458
## settlementVillage                                                -0.51604
## eduT1                                                             0.18247
## income1                                                          -0.05216
## regionRU: Central Federal District                                0.29634
## regionRU: North Caucasian federal district                       -0.01422
## regionRU: Volga; Privolzhsky Federal District                     0.15736
## regionRU: Urals Federal District                                 -0.28383
## regionRU: Far East Federal District                              -0.16103
## regionRU: Siberian Federal District                               0.22390
## regionRU: South Federal District                                 -0.49261
##                                                                  Std. Error
## (Intercept)                                                         0.32573
## intinpolSomewhat interested                                         0.19349
## intinpolNot very interested                                         0.19207
## intinpolNot at all interested                                       0.22336
## settlementRegional center                                           0.22548
## settlementDistrict center                                           0.21698
## settlementAnother city, town (not a regional or district center)    0.35755
## settlementVillage                                                   0.22827
## eduT1                                                               0.11323
## income1                                                             0.02802
## regionRU: Central Federal District                                  0.20388
## regionRU: North Caucasian federal district                          0.28489
## regionRU: Volga; Privolzhsky Federal District                       0.20116
## regionRU: Urals Federal District                                    0.24005
## regionRU: Far East Federal District                                 0.29521
## regionRU: Siberian Federal District                                 0.21403
## regionRU: South Federal District                                    0.24191
##                                                                  z value
## (Intercept)                                                        2.881
## intinpolSomewhat interested                                       -2.365
## intinpolNot very interested                                       -3.281
## intinpolNot at all interested                                     -6.268
## settlementRegional center                                         -2.038
## settlementDistrict center                                         -4.028
## settlementAnother city, town (not a regional or district center)  -2.726
## settlementVillage                                                 -2.261
## eduT1                                                              1.611
## income1                                                           -1.862
## regionRU: Central Federal District                                 1.453
## regionRU: North Caucasian federal district                        -0.050
## regionRU: Volga; Privolzhsky Federal District                      0.782
## regionRU: Urals Federal District                                  -1.182
## regionRU: Far East Federal District                               -0.545
## regionRU: Siberian Federal District                                1.046
## regionRU: South Federal District                                  -2.036
##                                                                  Pr(>|z|)    
## (Intercept)                                                       0.00397 ** 
## intinpolSomewhat interested                                       0.01802 *  
## intinpolNot very interested                                       0.00103 ** 
## intinpolNot at all interested                                    3.66e-10 ***
## settlementRegional center                                         0.04159 *  
## settlementDistrict center                                        5.62e-05 ***
## settlementAnother city, town (not a regional or district center)  0.00642 ** 
## settlementVillage                                                 0.02378 *  
## eduT1                                                             0.10707    
## income1                                                           0.06261 .  
## regionRU: Central Federal District                                0.14609    
## regionRU: North Caucasian federal district                        0.96018    
## regionRU: Volga; Privolzhsky Federal District                     0.43407    
## regionRU: Urals Federal District                                  0.23706    
## regionRU: Far East Federal District                               0.58542    
## regionRU: Siberian Federal District                               0.29552    
## regionRU: South Federal District                                  0.04172 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2357.9  on 1735  degrees of freedom
## Residual deviance: 2247.5  on 1719  degrees of freedom
## AIC: 2281.5
## 
## Number of Fisher Scoring iterations: 4

We dropped out age. From the content point of view, both younger and older can be equally involved in lawful demonstrations depending on the topic of discussion. However, there are two more variables which p-values were considered to be insignificant, so let`s have a closer look on model building step by step.

It appears that adding eduT does not contribute to our model, so the final point to consider is to drop it. Although p-value of income1 was insignificant, it contributes to the model, so the variable will be preserved.

The final model to discuss is without eduT and age.

Choosing the best model

Due to AIC, the lower value was indicated by the second model, we can say that the second model (with eduT) is the best one.

Let`s consider variables importance more precisely:

Conclusion: The plot has proved that all the variables are important for our model (importance >0), so the final model is the second one.

Model equation

## Q211 ~ intinpol + settlement + eduT + income1 + region

\[ \begin{aligned} \log\left[ \frac { P( \operatorname{Q211} = \operatorname{1} ) }{ 1 - P( \operatorname{Q211} = \operatorname{1} ) } \right] &= \alpha + \beta_{1}(\operatorname{intinpol}_{\operatorname{Somewhat\ interested}}) + \beta_{2}(\operatorname{intinpol}_{\operatorname{Not\ very\ interested}})\ + \\ &\quad \beta_{3}(\operatorname{intinpol}_{\operatorname{Not\ at\ all\ interested}}) + \beta_{4}(\operatorname{settlement}_{\operatorname{Regional\ center}}) + \beta_{5}(\operatorname{settlement}_{\operatorname{District\ center}})\ + \\ &\quad \beta_{6}(\operatorname{settlement}_{\operatorname{Another\ city,\ town\ (not\ a\ regional\ or\ district\ center)}} \times \operatorname{region}_{\operatorname{settlementAnother\ city,\ town\ (not\ a\ al\ or\ district\ center)}}) + \beta_{7}(\operatorname{settlement}_{\operatorname{Village}}) + \beta_{8}(\operatorname{eduT}_{\operatorname{1}})\ + \\ &\quad \beta_{9}(\operatorname{income1}) + \beta_{10}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ Central\ Federal\ District}}) + \beta_{11}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ North\ Caucasian\ federal\ district}})\ + \\ &\quad \beta_{12}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ Volga;\ Privolzhsky\ Federal\ District}}) + \beta_{13}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ Urals\ Federal\ District}}) + \beta_{14}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ Far\ East\ Federal\ District}})\ + \\ &\quad \beta_{15}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ Siberian\ Federal\ District}}) + \beta_{16}(\operatorname{region}_{\operatorname{RU}} \times \operatorname{region}_{\operatorname{\ South\ Federal\ District}}) + \epsilon \end{aligned} \]

Model Interpretation

Coefficients` interpretation by odds-ratios

##                                                                         OR
## (Intercept)                                                      2.5557994
## intinpolSomewhat interested                                      0.6327662
## intinpolNot very interested                                      0.5324778
## intinpolNot at all interested                                    0.2466042
## settlementRegional center                                        0.6316389
## settlementDistrict center                                        0.4172492
## settlementAnother city, town (not a regional or district center) 0.3773508
## settlementVillage                                                0.5968790
## eduT1                                                            1.2001831
## income1                                                          0.9491730
## regionRU: Central Federal District                               1.3449239
## regionRU: North Caucasian federal district                       0.9858775
## regionRU: Volga; Privolzhsky Federal District                    1.1704140
## regionRU: Urals Federal District                                 0.7528927
## regionRU: Far East Federal District                              0.8512669
## regionRU: Siberian Federal District                              1.2509413
## regionRU: South Federal District                                 0.6110300
##                                                                      2.5 %
## (Intercept)                                                      1.3532650
## intinpolSomewhat interested                                      0.4320207
## intinpolNot very interested                                      0.3644688
## intinpolNot at all interested                                    0.1585151
## settlementRegional center                                        0.4047389
## settlementDistrict center                                        0.2716470
## settlementAnother city, town (not a regional or district center) 0.1848084
## settlementVillage                                                0.3803199
## eduT1                                                            0.9611032
## income1                                                          0.8982903
## regionRU: Central Federal District                               0.9033133
## regionRU: North Caucasian federal district                       0.5614864
## regionRU: Volga; Privolzhsky Federal District                    0.7901501
## regionRU: Urals Federal District                                 0.4692820
## regionRU: Far East Federal District                              0.4732048
## regionRU: Siberian Federal District                              0.8232027
## regionRU: South Federal District                                 0.3792655
##                                                                     97.5 %
## (Intercept)                                                      4.8565439
## intinpolSomewhat interested                                      0.9233994
## intinpolNot very interested                                      0.7747165
## intinpolNot at all interested                                    0.3808177
## settlementRegional center                                        0.9804156
## settlementDistrict center                                        0.6365019
## settlementAnother city, town (not a regional or district center) 0.7539667
## settlementVillage                                                0.9314048
## eduT1                                                            1.4983501
## income1                                                          1.0026211
## regionRU: Central Federal District                               2.0103054
## regionRU: North Caucasian federal district                       1.7188931
## regionRU: Volga; Privolzhsky Federal District                    1.7398356
## regionRU: Urals Federal District                                 1.2039454
## regionRU: Far East Federal District                              1.5099103
## regionRU: Siberian Federal District                              1.9064432
## regionRU: South Federal District                                 0.9800786

For now, we can draw conclusions about the direction of the effect produced by variables.However, we will not interpret it for education and income, since they appear to be insignificant.

Conclusion

interest in politics

• The probability that a person will attend a lawful demonstration decreases by the factor of 0.63 for citizens who is somewhat interested in politics compared to ones who very interested in politics.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.53 for citizens who is not very interested in politics compared to ones who very interested in politics.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.25 for citizens who is not at all interested in politics compared to ones who very interested in politics.

settlement

• The probability that a person will attend a lawful demonstration decreases by the factor of 0.63 for citizens who live in regional center compared to ones who lives in capital city.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.42 for citizens who live in district center compared to ones who lives in capital city.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.38 for citizens who live in another city, town compared to ones who lives in capital city.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.6 for citizens who live in a village compared to ones who lives in capital city.

district

• The probability that a person will attend a lawful demonstration increases by the factor of 1.34 for citizens who live in Central Federal District compared to ones who live in North West Federal District.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.98 for citizens who live in North Caucasian federal district compared to ones who live in North West Federal District.
• The probability that a person will attend a lawful demonstration increases by the factor of 1.17 for citizens who live in Volga; Privolzhsky Federal District compared to ones who live in North West Federal District.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.75 for citizens who live in Urals Federal District compared to ones who live in North West Federal District.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.85 for citizens who live in Far East Federal District compared to ones who live in North West Federal District.
• The probability that a person will attend a lawful demonstration increases by the factor of 1.25 for citizens who live in Siberian Federal District compared to ones who live in North West Federal District.
• The probability that a person will attend a lawful demonstration decreases by the factor of 0.61 for citizens who live in South Federal District compared to ones who live in North West Federal District.

Reporting average marginal effects

## [1] 3.770737

Conclusion: Living in Central Federal District/ Volga; Privolzhsky Federal District/Siberian Federal District or being interested in politics or living in capital cities is associated with higher probability of attending lawful demonstrations.

Detailed Conclusion

interest in politics

• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.31 lower for the individual who has not at all interested in politics than for one who is very interested in politics.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.15 lower for the individual who has not very interested in politics than for one who is very interested in politics.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.1 lower for the individual who has somewhat interested in politics than for one who is very interested in politics.

region

• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.07 higher for the individual who live in Central Federal District than for one who lives in North West Federal District.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.03 lower for the individual who live in Far East Federal District than for one who lives in North West Federal District.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.0003 lower for the individual who live in North Caucasian federal district than for one who lives in North West Federal District.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.05 higher for the individual who live in Siberian Federal District than for one lives in North West Federal District.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.05 higher for the individual who live in South Federal District than for one who lives in North West Federal District.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.06 lower for the individual who lives in Urals Federal District than for one who lives in North West Federal District.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.03 higher for the individual who lives in Volga; Privolzhsky Federal District than for one who lives in North West Federal District.

settlement

• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.23 lower for the individual who lives in another city, town (not a regional or district center) than for one who lives in capital city.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.2 lower for the individual who lives in District center than for one who lives in capital city.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.1 lower for the individual who lives in Regional center than for one who lives in capital city.
• for two hypothetical individuals with average values on income (3.77), the predicted probability of attending lawful demonstration is 0.1 lower for the individual who lives in Village than for one who lives in capital city.

Predicting the value of the outcome given the average and extreme values of predictors

##    xvals     yvals     upper     lower
## 1  0.000 0.5361993 0.6270888 0.4453099
## 2  0.375 0.5313313 0.6198545 0.4428080
## 3  0.750 0.5264572 0.6128251 0.4400894
## 4  1.125 0.5215782 0.6060223 0.4371340
## 5  1.500 0.5166950 0.5994672 0.4339228
## 6  1.875 0.5118086 0.5931795 0.4304377
## 7  2.250 0.5069200 0.5871773 0.4266627
## 8  2.625 0.5020300 0.5814754 0.4225846
## 9  3.000 0.4971397 0.5760856 0.4181938
## 10 3.375 0.4922499 0.5710151 0.4134846
## 11 3.750 0.4873615 0.5662669 0.4084562
## 12 4.125 0.4824756 0.5618393 0.4031120
## 13 4.500 0.4775931 0.5577261 0.3974601
## 14 4.875 0.4727148 0.5539169 0.3915127
## 15 5.250 0.4678417 0.5503982 0.3852853
## 16 5.625 0.4629748 0.5471533 0.3787963
## 17 6.000 0.4581149 0.5441638 0.3720660
## 18 6.375 0.4532629 0.5414101 0.3651158
## 19 6.750 0.4484199 0.5388721 0.3579676
## 20 7.125 0.4435865 0.5365296 0.3506434

Overall, the higher income is associated with lower predicted attendance of lawful demonstrations.

Prediction on the best model and model fit

In-sample model fit

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 838 500
##          1 175 223
##                                           
##                Accuracy : 0.6112          
##                  95% CI : (0.5878, 0.6342)
##     No Information Rate : 0.5835          
##     P-Value [Acc > NIR] : 0.0102          
##                                           
##                   Kappa : 0.145           
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.8272          
##             Specificity : 0.3084          
##          Pos Pred Value : 0.6263          
##          Neg Pred Value : 0.5603          
##              Prevalence : 0.5835          
##          Detection Rate : 0.4827          
##    Detection Prevalence : 0.7707          
##       Balanced Accuracy : 0.5678          
##                                           
##        'Positive' Class : 0               
## 

Here, predicted and observed outcomes are compared in confusion matrix. A classification is correct when predicted class of the observation coincides with its observed class. In other cases the prediction is wrong and observations are misclassified.

• In this model, 1061 out of 1736 citizens were correctly classified.
• Accuracy is equal to 0.61 which is not really high and indicated bad model performance.
• Sensitivity is high, so that the model is good for predicting those who would not attend lawful demonstration.
• We can see that Specificity of our model is equal to 0.3, which is really low. That means that the model works bad for predicting those who would attend lawful demostrations.

Out-of-sample model fit

Next, we want to check whether our model is overfitted or not.

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 156  83
##          1  56  45
##                                           
##                Accuracy : 0.5912          
##                  95% CI : (0.5368, 0.6439)
##     No Information Rate : 0.6235          
##     P-Value [Acc > NIR] : 0.90052         
##                                           
##                   Kappa : 0.0912          
##                                           
##  Mcnemar's Test P-Value : 0.02743         
##                                           
##             Sensitivity : 0.7358          
##             Specificity : 0.3516          
##          Pos Pred Value : 0.6527          
##          Neg Pred Value : 0.4455          
##              Prevalence : 0.6235          
##          Detection Rate : 0.4588          
##    Detection Prevalence : 0.7029          
##       Balanced Accuracy : 0.5437          
##                                           
##        'Positive' Class : 0               
## 

The model`s performance on a test sample remains quite same, which means that we are likely to avoid overfitting.

Model quality

## Area under the curve: 0.5397

The model reports bad quality, since values are under 0.8

Diagnostics

##            Test stat Pr(>|Test stat|)
## intinpol                             
## settlement                           
## eduT                                 
## income1       0.7792           0.3774
## region

As we can see, predictors are not linear, so the assumption is kept

##                GVIF Df GVIF^(1/(2*Df))
## intinpol   1.092152  3        1.014800
## settlement 1.659764  4        1.065383
## eduT       1.130039  1        1.063033
## income1    1.151644  1        1.073147
## region     1.709112  7        1.039026

No multicollinearity since GVIF < 10, so the assumption is kept.