How to interpret mixed level logistic regression with contrast coding?

Question

I'm currently trying to interpret several mixed-level logistic regressions with contrast coding and it is my first time using this method.

My main research of interest is the intercept, which is whether participants are more likely to choose Person A or B, and each participant made this decision 4 times.

In my data frame, Person A is coded as 1, Person B is coded as 2.

Here is what the results look like:

## MLM Step 3 -- Add fixed effects
set_sum_contrasts() # Contrast coding

m3 <- glmer(Decision ~ `Allocate Scenario` + (1 | ID), 
            data = long_cleandata, 
            family = binomial(link="logit"),
            control = glmerControl(optimizer = "bobyqa"))

summary(m3)

#   AIC      BIC   logLik deviance df.resid 
# 489.1    500.9   -241.6    483.1      373 

# Scaled residuals: 
#     Min      1Q  Median      3Q     Max 
# -1.3330 -0.6002 -0.4246  0.7502  1.6660 

# Random effects:
#   Groups Name        Variance Std.Dev.
#     ID     (Intercept) 1.384    1.176   
#   Number of obs: 376, groups:  ID, 94

# Fixed effects:
#                       Estimate Std. Error z value Pr(>|z|)   
# (Intercept)           -0.5026     0.1730  -2.905  0.00367 **
# `Allocate Scenario`1  -0.2007     0.1192  -1.683  0.09236 . 
# ---
#  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Correlation of Fixed Effects:
#            (Intr)
# `AllcScnr`1 0.033

Can I interpret the intercept (log(Odds)= -0.5026, Odds = 0.6049557) as follows:

The intercept represents the average log odds of person B's probability of receiving £20. After the exponentiating, the odds of person B's probability of receiving £20 are 0.60, which means that, on average, participants in our experiment are (1/0.604) 1.65 times more likely to offer £20 to Person A.

Thank you so much for your help!

Theo C. · Answer

It's kinda hard to understand without knowing what Allocate Scenario1 stands for. Is it a binary variable ? Discrete? continuous? positive only?

Anyway those two statements are false unless Allocate Scenario1 is normally distributed around 0.

The intercept represents the average log odds of person B's probability of receiving £20

and

on average, participants in our experiment are (1/0.604) 1.65 times more likely to [...]

My understanding is that the intercept represent the log(odds) that person B is chosen when there is no particular scenario influencing that decision ; when 'Scenario' is NULL. I'm gonna guess that is not the case on average in your experiment as it is rare. The fact that Allocate Scenario1 coefficient is not significant doesn't change that.

If you want the odds of A in your experiment just calculate it from the initial dataset, you don't need a model for that. But that would be limited to your experiment and specific to the different scenarios you presented and their frequency in the study.

How to interpret mixed level logistic regression with contrast coding?

1 Answers