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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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  • $\begingroup$ I think that the interaction (in which case I would assume as the term gonad:nnd) has no interpretative meaning, but rather only tells you if the rate of change in the probability of spawning as explained by the continuous variable nnd is significantly affected by the variable gonad. That is, is the rate of change significantly different across the three categories of gonad or not.:) $\endgroup$ – math_stat_enthusiast Jan 2 '14 at 6:48
  • $\begingroup$ The idea of using systematic predictions is very good but it involves varying nnd too. $\endgroup$ – Michael M Jan 2 '14 at 6:54
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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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