# Solved – How to interpret interaction continuous variables in logistic regression

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?

Contents

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`.