# difficulty in interpreting significance of logistic regression with multiple categorical variables

I am trying to do a logistic regression in order to check for statistical significance among my multiple categorical variables.

I have the following independent variables (IV): (1) Beta factor - Regression coefficient, measures the volatility against the benchmark (2) Time Dummy - 1 if event after 2017, 0 otherwise (3) ESG Percentil - 10 Categories with increment of 10% until 100% starting from 0 (4) GICS Industry Code - Global Industry Classification Standard (5) Category Dummy - 1 if Industry is manufacturing, 0 otherwise

My Dependent variable is a dummy variable that is 1 if the cumulative abnormal return (CAR) is positive and 0 otherwise.

My goal is to see which categories are relevant in order to create positive CAR. E.g. I want to check whether being in the Energy Sector has positive influence on positive CAR.

However, I have difficulties in interpreting my results. As e.g. for the reference group no p-value is given, I don't know if the reference group is statistically significant.

This is the head of my data:

# A tibble: 6 x 6
CAR_dummy  Beta time_dummy ESG_Percentil Category GICS_SECTOR
<dbl> <dbl>      <dbl>         <dbl>    <dbl>       <dbl>
1         0 0.789          1            20        1          15
2         1 1.50           1            30        1          15
3         1 1.25           1            20        1          15
4         0 0.851          1            40        1          15
5         1 0.831          1            90        0          40
6         1 1.35           1            80        0          40


Now I have run this code to create my logistic regression:

mylogit_all = glm(as.factor(CAR_dummy) ~   Beta + as.factor(time_dummy)  +  as.factor(ESG_Percentil) + as.factor(Category) + as.factor(GICS_SECTOR), data=data_logit, family=binomial(link="logit"))
summary(mylogit_all)


The result:

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                  0.7692     0.4956   1.552 0.120681
Beta                        -0.7968     0.1386  -5.750 8.92e-09 ***
as.factor(time_dummy)1       0.2833     0.1349   2.100 0.035689 *
as.factor(ESG_Percentil)10   0.2876     0.4037   0.712 0.476315
as.factor(ESG_Percentil)20   0.6152     0.3857   1.595 0.110751
as.factor(ESG_Percentil)30   0.5291     0.3706   1.428 0.153430
as.factor(ESG_Percentil)40   0.5197     0.3627   1.433 0.151886
as.factor(ESG_Percentil)50   0.5665     0.3609   1.570 0.116527
as.factor(ESG_Percentil)60   0.6375     0.3628   1.757 0.078938 .
as.factor(ESG_Percentil)70   0.6025     0.3625   1.662 0.096527 .
as.factor(ESG_Percentil)80   0.6441     0.3592   1.793 0.073002 .
as.factor(ESG_Percentil)90   0.4063     0.3532   1.150 0.250060
as.factor(Category)1         0.1156     0.1844   0.627 0.530705
as.factor(GICS_SECTOR)15    -1.4278     0.3326  -4.293 1.76e-05 ***
as.factor(GICS_SECTOR)20    -0.9949     0.3203  -3.106 0.001894 **
as.factor(GICS_SECTOR)25    -1.0439     0.3343  -3.123 0.001791 **
as.factor(GICS_SECTOR)30    -0.6618     0.3391  -1.952 0.050996 .
as.factor(GICS_SECTOR)35    -1.3176     0.3395  -3.881 0.000104 ***
as.factor(GICS_SECTOR)40    -0.6012     0.3646  -1.649 0.099133 .
as.factor(GICS_SECTOR)45    -1.3939     0.3865  -3.606 0.000311 ***
as.factor(GICS_SECTOR)50    -0.9954     0.3919  -2.540 0.011085 *
as.factor(GICS_SECTOR)55    -0.8833     0.3529  -2.503 0.012308 *
as.factor(GICS_SECTOR)60    -0.6511     0.3835  -1.698 0.089566 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 2563.6  on 1850  degrees of freedom
Residual deviance: 2486.9  on 1828  degrees of freedom
(1 observation deleted due to missingness)
AIC: 2532.9

Number of Fisher Scoring iterations: 4


In my understanding, all these significances of the coefficients are created by comparing to the reference group. In this case it must be the group with time dummy = 0, ESG_percentil = 0, Category = 0, GICS_SECTOR = 10.

Thus, GICS_SECTOR = 15 has exp(-1.4278) higher odds in creating positive CAR than GICS_SECTOR = 10. But I want to show that GICS_SECTOR = X is more relevant than GICS_SECTOR = Y. On the other hand, there must be at least one group to compare with.

I have difficulties in interpreting this result, as how do I know if GICS_SECTOR = 10 (Energy) is statistically significant for CAR?

I tried this model with one hot encoding of GICS_SECTOR in order to get also a p-value for GICS_SECTOR = 10. However, one row is getting "NA" probably because it can be explained by the other variables.

mylogit_all = glm(as.factor(CAR_dummy) ~   Beta + as.factor(time_dummy)  +  as.factor(ESG_Percentil) + as.factor(Category) +
10+15+20+25+30+35+40+45+50+55 +60, data=data_logit, family=binomial(link="logit"))


Also, I factorized the percentile Ranking in ESG_Percentil in order to see from which percentile "it gets more relevant". Would this be a valid approach?

I am very happy if someone can shed a bit of light on my problem!