I'm hoping someone can help clarify a few things for me.
I ran some relatively simple logistic regressions in r and am having trouble with interpretation. I'm interested in the effects of elevation and a species diversity index on the presence/absence of a disease in individual animals.
I ran a simple model of:
Result~Elevation+Diversity which gave this result
Call: glm(formula = Test_Result ~ Elevation + Simpsons_Diversity, family = binomial, data = XXXXXX) Deviance Residuals: Min 1Q Median 3Q Max -0.8141 -0.6984 -0.5317 -0.4143 2.3337 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.118e+00 1.594e-01 -13.289 < 2e-16 Elevation 1.316e-04 2.247e-05 5.855 4.76e-09 Simpsons_Diversity -9.907e-01 2.725e-01 -3.635 0.000278 Null deviance: 3015.2 on 3299 degrees of freedom Residual deviance: 2923.6 on 3297 degrees of freedom AIC: 2929.6
I have a strong suspicion that diversity decreases with increasing elevation which I have confirmed although the relationship isn't quite as strong as I thought. When I run a model with an interaction term
elevation*diversity I get:
Call: glm(formula = Test_Result ~ Elevation_1000 + Simpsons_Diversity_100 + Elevation_1000 * Simpsons_Diversity_100, family = binomial, data = XXXXXXX) Deviance Residuals: Min 1Q Median 3Q Max -0.7908 -0.6959 -0.5437 -0.3963 2.4215 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.014422 0.179507 -11.222 < 2e-16 Elevation_1000 0.112466 0.027433 4.100 4.14e-05 Simpsons_Diversity_100 -0.015851 0.005780 -2.743 0.0061 Elevation_1000:Simpsons_Diversity_100 0.001408 0.001200 1.173 0.2406 Null deviance: 3015.2 on 3299 degrees of freedom Residual deviance: 2922.2 on 3296 degrees of freedom AIC: 2930.2 Number of Fisher Scoring iterations: 5
Showing that adding the interaction term doesn't really help the fit of the model (AIC = 2930) and the interaction term itself is not significant (p-value=0.24).
Am I on the right track so far?
If I am, I understand how to convert coefficients to odds ratios and interpret those. My main question is can I plot the predicted probabilities for a combination of elevation and diversity where each variable is allowed to vary? Or is this essentially plotting the interaction?
I was able to create a dataframe where I varied elevation and diversity and I used my simple non-interaction model to obtain predicted probabilities using the PREDICT fuction) for those combinations, but I want to make sure that I am doing things correctly. I've attached the plot of predicted probs for different levels of diversity.