I am testing the following models. Volumes were purposely log10 transformed to examine brain allometry.
Model_Age_by_Sex <- lm(Grey_Matter_Volume_log ~ TBV_log * Age * sex, data = Data_1) Model_Age_by_Sex_Scaled <- lm(scale(Grey_Matter_Volume_log) ~ scale(TBV_log) * scale(Age) * sex, data = Data_1) summary(Model_Age_by_Sex)$coefficients Estimate Std. Error t value Pr(>|t|) (Intercept) 0.4874303644 0.1828868843 2.6652013 7.700986e-03 TBV_log 0.8809958273 0.0302474221 29.1263111 2.398416e-182 Age -0.0024949875 0.0029438211 -0.8475337 3.967088e-01 sexMale 0.6302910995 0.2639808852 2.3876392 1.696708e-02 TBV_log:Age 0.0003064347 0.0004871135 0.6290828 5.293027e-01 TBV_log:sexMale -0.1043227758 0.0434873643 -2.3989216 1.645339e-02 Age:sexMale -0.0100807480 0.0041958802 -2.4025347 1.629180e-02 TBV_log:Age:sexMale 0.0016541670 0.0006916066 2.3917747 1.677718e-02 summary(Model_Age_by_Sex_Scaled)$coefficients Estimate Std. Error t value Pr(>|t|) (Intercept) 0.068316452 0.004044650 16.8905709 1.601447e-63 scale(TBV_log) 0.949059885 0.004016238 236.3056916 0.000000e+00 scale(Age) -0.120918626 0.004028183 -30.0181524 2.733358e-193 sexMale -0.137960804 0.005930699 -23.2621491 5.528708e-118 scale(TBV_log):scale(Age) 0.002418004 0.003843698 0.6290828 5.293027e-01 scale(TBV_log):sexMale -0.001284456 0.005791493 -0.2217833 8.244850e-01 scale(Age):sexMale -0.009004298 0.005775597 -1.5590245 1.190079e-01 scale(TBV_log):scale(Age):sexMale 0.013052642 0.005457304 2.3917747 1.677718e-02
I want to analyze the standardized beta because my variables are on different scales and because I want to be able to say that the age effect for one brain volume was greater than for another, for instance.
When I scale my continuous variables with the scale function in R, the estimates, standard errors and p-values change. This is to be expected considering that I center my variables and am interested in an interaction (e.g. Standardized estimates give different p-value with a glmer/lmer).
However, some effects only become significant after I scale my variables. For instance, my age (p = 2.73e-193) and sex (p = 5.52e-118) main effects are not significant when my DV and IVs are not scaled but becomes very significant when my variables are scaled.
What should I do when the p-value is significant for my standardized output but not my unstandardized output?