R - Logistic Regression with Control Variables - r

Question

I just started to get into R for data analysis (previously I just used SPSS or Excel).
Currently, I am trying to run a logistic regression with one dependent and 5 independent while controlling for 3 variables.
My current attempt is:
reg_model <- glm(formula = Dependent ~ Independent1 + Independent2 + Independent3 + Independent4 + Independent5, family = binomial(), data = df)
I am not sure how (or where) to insert the 3 control variables into the model because just adding the 3 control variables as independent variables into the model seems wrong to me (or am I wrong here?).

Answer 1

You can control for potential confounders by adding them as independent variables into the model on the right-hand side of the formula.
Note that the estimate (effect size) of the Graduate Record Exam (GRE) score is lower in the second model after controlling for the grade point average (GPA), which is correlated to GRE:
library(readr)
# gre: Graduate Record Exam scores
# gpa: grade point average
data <- read_csv("https://stats.idre.ucla.edu/stat/data/binary.csv")
#>
#> ── Column specification ────────────────────────────────────────────────────────
#> cols(
#> admit = col_double(),
#> gre = col_double(),
#> gpa = col_double(),
#> rank = col_double()
#> )
data
#> # A tibble: 400 x 4
#> admit gre gpa rank
#> <dbl> <dbl> <dbl> <dbl>
#> 1 0 380 3.61 3
#> 2 1 660 3.67 3
#> 3 1 800 4 1
#> 4 1 640 3.19 4
#> 5 0 520 2.93 4
#> 6 1 760 3 2
#> 7 1 560 2.98 1
#> 8 0 400 3.08 2
#> 9 1 540 3.39 3
#> 10 0 700 3.92 2
#> # … with 390 more rows
model1 <- glm(admit ~ gre, data = data, family = "binomial")
summary(model1)
#>
#> Call:
#> glm(formula = admit ~ gre, family = "binomial", data = data)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -1.1623 -0.9052 -0.7547 1.3486 1.9879
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.901344 0.606038 -4.787 1.69e-06 ***
#> gre 0.003582 0.000986 3.633 0.00028 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 499.98 on 399 degrees of freedom
#> Residual deviance: 486.06 on 398 degrees of freedom
#> AIC: 490.06
#>
#> Number of Fisher Scoring iterations: 4
# gre and gpa are correlated. Lets's control for them!
cor(data)
#> admit gre gpa rank
#> admit 1.0000000 0.1844343 0.17821225 -0.24251318
#> gre 0.1844343 1.0000000 0.38426588 -0.12344707
#> gpa 0.1782123 0.3842659 1.00000000 -0.05746077
#> rank -0.2425132 -0.1234471 -0.05746077 1.00000000
model2 <- glm(admit ~ gre + gpa, data = data, family = "binomial")
summary(model2)
#>
#> Call:
#> glm(formula = admit ~ gre + gpa, family = "binomial", data = data)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -1.2730 -0.8988 -0.7206 1.3013 2.0620
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.949378 1.075093 -4.604 4.15e-06 ***
#> gre 0.002691 0.001057 2.544 0.0109 *
#> gpa 0.754687 0.319586 2.361 0.0182 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 499.98 on 399 degrees of freedom
#> Residual deviance: 480.34 on 397 degrees of freedom
#> AIC: 486.34
#>
#> Number of Fisher Scoring iterations: 4
Created on 2021-10-01 by the reprex package (v2.0.1)