I'm interested in the effect of a categorical variable X (let's say the application of heat) on continuous variable Y (the expression level of a particular gene). I have measurements of Y for samples of several different types of cells from several different subjects under both conditions of X. I'm interested in the effect of heatshock on the expression of the gene and am not interested in the cell type (a fixed effect?). However I do expect that the cell type may affect the baseline expression of my gene and interact with the effect of heatshock (i.e. the strength of the effect of heatshock may vary depending on the cell type, but should always be in the same direction).
I used lme4 in R as follows:
m <- lmer( Expression ~ HeatCondition * Celltype +(1|Subject), data=dat)
dat.null = lmer(Expression ~ Celltype +(1|Subject), data=dat,REML=FALSE)
dat.model = lmer(Expression ~ HeatCondition * Celltype +(1|Subject), data=dat,REML=FALSE)
There was a significant difference in the likelihood of my two models. However, I'm unsure how to report the effect of heatshock. Do I report the estimated fixed effect and standard error of HeatCondition or HeatCondition:Celltype? Or am I going about this all the wrong way and should be looking at both main effects and the interaction separately like an ANOVA? If somebody could set me straight, I'd much appreciate it.
Also, would anything change if instead of cell type, I had an ordinal or a discrete variable, such as an approximate co-ordinate or age?
(N.B. - details of the variables are changed for simplicity, so please take my word for it on the nature of the variables and their relationships if there's any inconsistency in that regard.)