# Contrasts in logistic regression using R

I am trying to use contrasts in a logistic regression using the lme4 package. I have two between-subject categorical variables (both with 2 levels). The first distinguishes between groups 1 and 2; the second between groups A and B.
I prepared a single column with between-subject categorical variable with 4 levels: 1A, 1B, 2A, and 2B. I would like to see the effect of those variables on 1 binary variable. We have a strong a priori linear hypothesis: i.e. 1A > 1B > 2A > 2B.

# Data frame is d
# Column to predict is BD
# Column with 4 groups is IV with four level (1A, 1B, 2A and 2B).

# Factorize IV column
d$$IV <- factor(d$$IV, levels = c("1A", "1B" , "2A", "2B"), ordered = TRUE)


I encoded 2 first contrast to test both between-group variables.

# "Group effects" contrast creation
Contrast1 <- c(-0.5, -0.5, 0.5, 0.5) # Test the difference between groups 1 and 2
Contrast2 <- c(-0.5, 0.5, -0.5, 0.5) # Test the difference between groups A and B


I would now like to add a linear contrast to confirm our main hypothesis

# Linear contrast
Contrast3 <- c(-0.6708204, -0.2236068, 0.2236068, 0.6708204)
# I chose these numbers because they were given to me when I simply used the contrasts() function on the
# ordered factor

# Contrast matrices creation
matCont <- matrix(c(Contrast1, Contrast2, Contrast3), ncol = 3)
colnames(matCont) <- c("1vs2", "AvsB", "Linear")
contrasts(d\$IV) <- matCont


To run my logistic regression, I use the glm() function:

RegLog <- glm(BD ~ IV, data = d, family = binomial(link = 'logit'))
summary(RegLog)


This command returns expected values for contrasts 1 and 2, but not for the linear contrast (where I only get NAs with the following message Coefficients: (1 not defined because of singularities)).

So I understand this "singularity" error. What poses me problem is that when I use the exact same regression on the standard contrast given by the contrasts() function (linear, quadratic, and cubic), I get a significant linear contrast.
Do these discrepancies between both techniques come from the fact that I mixed different contrasts into 1 analysis (linear and between-group)? Therefore, should I run two separate analyses, one with the between-group (and adding an interaction contrast) and one with the linear, quadratic, and cubic contrasts? I did not do so in an effort to minimize the amount of different analyze (and I do not expect a significant quadratic or cubic contrast at all).

• There is no real way to treat the grouping variable as ordered (and not necessarily quadratic) without using a Bayesian model. The R brms package respects ordinal predictors. Sep 21 at 11:44