I have a logistic regression model with several variables and one of those variables (called x3 in my example below) is not significant. However, x3 should remain in the model because it is scientifically important.
Now, x3 is continuous and I want to create a plot of the predicted probability vs x3. Even though x3 is not statistically significant, it has an effect on my outcome and therefore it has an effect on the predicted probability. This means that I can see from the graph, that the probability changes with increasing x3. However, how should I interpret the graph and the change in the predicted probability, given that x3 is indeed not statistically significant?
Below is a simulated data in R set to illustrate my question. The graph also contains a 95% confidence interval for the predicted probability (dashed lines):
> set.seed(314) > n <- 300 > x1 <- rbinom(n,1,0.5) > x2 <- rbinom(n,1,0.5) > x3 <- rexp(n) > logit <- 0.5+0.9*x1-0.5*x2 > prob <- exp(logit)/(1+exp(logit)) > y <- rbinom(n,1,prob) > > model <- glm(y~x1+x2+x3, family="binomial") > summary(model) Call: glm(formula = y ~ x1 + x2 + x3, family = "binomial") Deviance Residuals: Min 1Q Median 3Q Max -2.0394 -1.1254 0.5604 0.8554 1.4457 Coefficients: Estimate Std. Error z value Pr( >|z|) (Intercept) 1.1402 0.2638 4.323 1.54e-05 *** x1 0.8256 0.2653 3.112 0.00186 ** x2 -1.1338 0.2658 -4.266 1.99e-05 *** x3 -0.1478 0.1249 -1.183 0.23681 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 373.05 on 299 degrees of freedom Residual deviance: 341.21 on 296 degrees of freedom AIC: 349.21 Number of Fisher Scoring iterations: 3 > > dat <- data.frame(x1=1, x2=1, x3=seq(0,5,0.1)) > preds <- predict(model, dat,type = "link", se.fit = TRUE ) > critval <- 1.96 > upr <- preds$fit + (critval * preds$se.fit) > lwr <- preds$fit - (critval * preds$se.fit) > fit <- preds$fit > > fit2 <- mod$family$linkinv(fit) > upr2 <- mod$family$linkinv(upr) > lwr2 <- mod$family$linkinv(lwr) > > plot(dat$x3, fit2, lwd=2, type="l", main="Predicted Probability", ylab="Probability", xlab="x3", ylim=c(0,1.00)) > lines(dat$x3, upr2, lty=2) > lines(dat$x3, lwr2, lty=2)