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?

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#### 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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