This might be a trivial question but I don't know where to find answers. I'm wondering when using glm() for logistic regression in R, if the response variable Y has factor values 1 or 2, does the result of glm() correspond to logit(P(Y=1)) or logit(P(Y=2))? What if Y has logical values TRUE or FALSE?
Why not just test it yourself?
output_bool <- c(rep(c(TRUE, FALSE), c(25, 75)), rep(c(TRUE, FALSE), c(75, 25)))
output_num <- c(rep(c(2, 1), c(25, 75)), rep(c(2, 1), c(75, 25)))
output_fact <- factor(output_num)
var <- rep(c("unlikely", "likely"), each = 100)
glm(output_bool ~ var, binomial)
#>
#> Call: glm(formula = output_bool ~ var, family = binomial)
#>
#> Coefficients:
#> (Intercept) varunlikely
#> 1.099 -2.197
#>
#> Degrees of Freedom: 199 Total (i.e. Null); 198 Residual
#> Null Deviance: 277.3
#> Residual Deviance: 224.9 AIC: 228.9
glm(output_num ~ var, binomial)
#> Error in eval(family$initialize): y values must be 0 <= y <= 1
glm(output_fact ~ var, binomial)
#>
#> Call: glm(formula = output_fact ~ var, family = binomial)
#>
#> Coefficients:
#> (Intercept) varunlikely
#> 1.099 -2.197
#>
#> Degrees of Freedom: 199 Total (i.e. Null); 198 Residual
#> Null Deviance: 277.3
#> Residual Deviance: 224.9 AIC: 228.9
So, we get the correct answer if we use TRUE and FALSE, an error if we use 1 and 2 as numbers, and the correct result if we use 1 and 2 as a factor with two levels provided the TRUE value has a higher factor level than the FALSE. However, we have to be careful in how our factors are ordered or we will get the wrong result:
output_fact <- factor(output_fact, levels = c("2", "1"))
glm(output_fact ~ var, binomial)
#>
#> Call: glm(formula = output_fact ~ var, family = binomial)
#>
#> Coefficients:
#> (Intercept) varunlikely
#> -1.099 2.197
#>
#> Degrees of Freedom: 199 Total (i.e. Null); 198 Residual
#> Null Deviance: 277.3
#> Residual Deviance: 224.9 AIC: 228.9
(Notice the intercept and coefficient have flipped signs)
Created on 2020-06-21 by the reprex package (v0.3.0)