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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)

summary(m)

dat.null = lmer(Expression ~ Celltype +(1|Subject), data=dat,REML=FALSE)

dat.model = lmer(Expression ~ HeatCondition * Celltype +(1|Subject), data=dat,REML=FALSE)

anova(pv.null, pv.model)

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.)

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The intepretation of the fixed effects in a linear mixed model is the same as the intepretation of the coefficients of a linear regression model (or an ANOVA model).

P.s., it would be better to use the F-test (e.g., using the lmerTest package) rather than the likelihood ratio test, especially if your sample is small.

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  • $\begingroup$ Thank you, I appreciate your response and will look into the F-test. Unfortunately my stats is a bit too rusty for me to meaningfully apply the first part of your post to the questions I asked. My understanding of ANOVA is that the model should be specified as something like Exp ~ Condition + Type + Condition:Type. Is it valid in a linear mixed model to simply compare Exp~Type to Exp~Condition*Type as I have above (plus the random effects)? If so, is the difference between the null and hypothesised models described by the effect of condition or the interaction effect (or both or neither)? $\endgroup$ – Jess Feb 11 at 19:33
  • $\begingroup$ The random effects only capture the correlations in the repeated measurements, they do not affect the interpretation of the fixed effects in linear mixed models. The test you performed evaluates whether the main effect of HeatCondition and its interaction with CellType improve the fit of the model. $\endgroup$ – Dimitris Rizopoulos Feb 12 at 5:42

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