I have a problem with interpreting 2-way and 3-way interactions in lmer. My DV is height which is a continuous variable. All IVs are categorical variables. The first factor is animal, either rat or lion. The second factor is sex, either male or female. The third factor is color: red, white, or yellow. I get confused with interpreting the output:
Fixed effects: Estimate Std. Error t value (Intercept) 164.6888 7.8180 21.065 rat -14.1342 8.2889 -1.705 sexmale -16.0883 10.0071 -1.608 colorred 0.5776 6.2473 0.092 coloryellow -14.4048 6.1025 -2.360 rat:sexmale 15.3645 11.8567 1.296 rat:colorred 12.5258 4.4028 2.845 rat:coloryellow 10.3136 4.3196 2.388 sexmale:colorred 2.0272 5.2773 0.384 sexmale:coloryellow 5.7643 5.1669 1.116 rat:sexmale:colorred -5.5144 6.2838 -0.878 rat:sexmale:coloryellow 0.9735 6.1690 2.158
According to Vasishth et al. (2007), the significance of fixed effects can be judged from the absolute t value; if it is higher than 2, then that factor is significant. In interpreting this output, I choose only factors which are significant. Please check if my interpretations are correct:
coloryellow= The height of subjects are lower when they like yellow, and are higher if they like white.
rat:colorred= The effect of rat preference enhances the preference of red, and these two promote height of subjects.
rat:sexmale:coloryellow= The effect of rat preference, being male, enhances the preference of yellow, and subjects who like rat and yellow and are male have higher height.
From these interpretations, I would like to ask: if I would like to know the effect of
rat:sexmale:colorred compared to
rat:sexfemale:coloorred, do I have to run new statistics?