How to interpret effects of predictors with large confidence intervals in GLMM?

Question

(This question is somehow related to my previous one)

My aim is to find out about which effect several predictors have on my response variable, I am interested in the direction and magnitude of the effect. I am wondering how I should evaluate the effect and if I can ignore the p-values for the estimates for that matter.

My model is a GLMM (Gamma family with inverse link):

Response ~ P1 + P2 + P3 + P4 + P... + (1|Plot) + (1|Year) + (1|Plant ID)

Now to get an idea of the marginal effects of the predictors I plot them using plot_model from sjPlot:

Where do I go from here?

Am I okay to ignore p-values from the model and consider the direction and effect of each predictor in order to find out how my response variable is influenced? I. e. can I safely interpret that an increment in P1 or reduction in P2 will increase the response (all other predictors held constant at their means)? How would I deal with and communicate the uncertainty (large confidence intervals)?

Answer 1

No, you cannot simply

ignore p-values from the model and consider the direction and effect of each predictor

First of all, note the estimated fixed effect coefficients for P1 and P2, -0.042 and 0.025 compared to those for P3 and P4, -0.204 and -1.242 respectively. Are the point estimates -0.042 and 0.025 practically significant ?

If we form a 95% confident interval for P1 as -0.042 +/- 1.96* 0.035, we obtain the interval (-0.1106, 0.0266), so we can be 95% confident that this interval contains the true estimate of the association of P1 on the outcome. Since this overlaps 0 substantially, you cannot simply ignore the p value and report the effect size, since we cannot be confident that the true effect is positive, negative or zero. A similar argument applies to P2: A 95% confidence interval is (-0.066, 0.01616).

If the end points of these confidence intervals are not practically significant then it should be OK to simply report these intervals and note that the entire interval is not practically significant.

If the end points of these confidence intervals are practically significant, then the best that you can do is simply report the point estimates and the intervals.