I am running an experiment with 3 different factors arranged in a factorial arrangement 3x3x3 (randomized complete block design with 4 blocks). These experimental plots are also replicated spatially and temporally across 3 locations, and 3 years. Thus, there is a total of 9 siteyears (3 locations x 3 years) representing different growth environments. In order to study the effects of three fixed factors on response variable, I am using the mixed model below –
mixed.model <- lmer(rv ~ f1 + f2 + f3 + f1:f2 + f2:f3 + f3:f1 + (1|siteyear/block), data)
However, my supervisor asked if the effect of factors on response variable changes in different siteyears i.e. if there is an interaction between siteyears and factors (f1, f2, f3). I ran a simple linear model with siteyear as fixed factor (given below) to check for the interaction and found significant interaction of f1 and f2 with siteyear.
l.model <- lm (rv ~ f1 + f2 + f3 + f1:f2 + f2:f3 + f3:f1 + siteyear + siteyear:f1 + siteyear:f2 + siteyear:f3, data)
My main question is that is the mixed model still valid in the presence of interaction of fixed effect with random effect (siteyear)? My understanding is that, by including siteyear as random effect, the interaction is accounted for as well. Is that true, and can you please provide an explanation of how it happens? I am also wondering if there is information on such interaction in the output of mixed model, and that lm model was not required to check interaction. Thank you!