Logistic – How to Interpret Interaction of Continuous Variables in Logistic Regression

continuous datainteractioninterpretationlogisticregression

I am struggling to understand and interpret the interaction term in a logistic regression. The explanatory variables are temperature (categorical), gonad weight (continuous) and nnd (continuous). Below the reduced model: 

model2012nnd = glm(fullyspawned ~ temperature + gonad + nnd+gonad:nnd, 
                   family=quasibinomial(link = logit), data=spaw)
summary(model2012nnd)
# 
# Call:
# glm(formula = fullyspawned ~ temperature + gonad + nnd + gonad:nnd, 
#     family = quasibinomial(link = logit), data = spaw)
# 
# Deviance Residuals: 
#     Min       1Q   Median       3Q      Max  
# -1.6793  -0.3594  -0.2457  -0.0651   2.5984  
# 
# Coefficients:
#                        Estimate Std. Error t value Pr(>|t|)    
# (Intercept)              2.6262     2.1212   1.238 0.217638    
# temperature15.58928019   2.4317     0.6453   3.768 0.000237 ***
# gonad                   -1.5718     0.6597  -2.382 0.018466 *  
# nnd                     -2.4845     1.0782  -2.304 0.022593 *  
# gonad:nnd                0.6407     0.3124   2.051 0.042058 *  
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
# 
# (Dispersion parameter for quasibinomial family taken to be 0.7864476)
# 
#     Null deviance: 118.652  on 152  degrees of freedom
# Residual deviance:  79.596  on 148  degrees of freedom
# AIC: NA

How do I interpret this interaction? I set the variable gonad into three categories (low, medium, and high) and graphed the probability of fully spawning at temperature 1 and 2 for each level, to try to understand the output. Is this correct?

Best Answer

When nnd is 0 a unit change in gonad is associated with a $(\exp(-1.5718 ) - 1)*100\% \approx -79 \% $ decrease in the odds of fullyspawned.

For every unit increase in nnd this effect of gonad increases by $(\exp( 0.6407 ) - 1)*100\% \approx 90 \%$.

So, when nnd is 1 the odds ratio for gonad is $1.9^1 \times .21 \approx .4$, that is, a unit change in gonad is now associated with only a $-60\%$ decrease in odds of fullyspawned. When nnd is 2 the odds ratio for gonad is $1.9^2 \times .21 \approx .76$, that is, a unit change in gonad is now associated with only a $-24\%$ decrease in odds of fullyspawned.

There are various examples on how to interpret interaction terms in this kind of model here.

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