Which model in lme4 for a continuous dependent variable (0-1) with ordinal independent variables (1-4)?

Question

all my questions are already indicated in the title. I will simply provide you with how I constructed the model. Additionally, for this case, should I use PCA, MCA, or FAMD to reduce dimensions?

model <- lmer(Pe_ratio ~ var1 + var2 + var3 + var4 + (1| var5), data = data1)

Answer 1

This is on the borderline of a CrossValidated question ("what method and why?" is for CV, "how do I do it in R?" is for SO).

• if you have proportions between 0 and 1 and you know the denominators (i.e. you can frame the response as "k out of N trials") then it would be best to use glmer(..., family = "binomial")
• you could arcsin-square-root transform your proportions (although see Warton and Hui); if you don't have any exact zeros or ones, you could logit-transform your response
• you could use some form of a Beta-distributed response (or zero-one-inflated, or ordinal beta), but you'll have to use glmmTMB, brms, or some other package - glmer only handles classical (exponential family) GLMs
• R will automatically handle your ordered predictor variables by using orthogonal polynomial contrasts (see ?contr.poly)

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Warton, David I., and Francis K. C. Hui. “The Arcsine Is Asinine: The Analysis of Proportions in Ecology.” Ecology 92, no. 1 (August 3, 2010): 3–10. https://doi.org/10.1890/10-0340.1.