Solved – Two factor linear mixed effect model with multiple slopes (lmer)

lme4-nlmemixed modelr

I have data with two factors TREATMENT and TIME both with two levels and a dependent variable RATIO. Besides random intercept for subjects, I want to specify random slopes for both of the independent variables for the mixed effect model in R using lmer.

Currently I have the model

lmer(RATIO ~ TREATMENT + TIME + (1 + TREATMENT + TIME | SUBJECT), data=my.data)

and the following questions.

Is the above model syntactically correct for specifying different random slopes for treatment and time?
What could be the reason that the model does not converge, i.e. it gives the following warning?

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Thanks in advance

Best Answer

Strictly speaking the model you present is syntactically correct.

Usually convergence failures are due to model misspecification, or insufficient data for estimation.

We do not know how many data-points you have so that might be an issue. Here you are specifying a model that has correlations between the random slopes for TIME and TREATMENT. You might want to try a model that has no correlations between the slopes but has two intercepts, eg. lmer(RATIO ~ TREATMENT + TIME + (TREATMENT| SUBJECT) + (TIME | SUBJECT), data=my.data) and see if this is adequate for your purposes. (The 1 + are redundant so I omitted them)

Related Solutions

R – Using lmer for Repeated-Measures Linear Mixed-Effect Model

I think that your approach is correct. Model m1 specifies a separate intercept for each subject. Model m2 adds a separate slope for each subject. Your slope is across days as subjects only participate in one treatment group. If you write model m2 as follows it's more obvious that you model a separate intercept and slope for each subject

m2 <- lmer(Obs ~ Treatment * Day + (1+Day|Subject), mydata)

This is equivalent to:

m2 <- lmer(Obs ~ Treatment + Day + Treatment:Day + (1+Day|Subject), mydata)

I.e. the main effects of treatment, day and the interaction between the two.

I think that you don't need to worry about nesting as long as you don't repeat subject ID's within treatment groups. Which model is correct, really depends on your research question. Is there reason to believe that subjects' slopes vary in addition to the treatment effect? You could run both models and compare them with anova(m1,m2) to see if the data supports either one.

I'm not sure what you want to express with model m3? The nesting syntax uses a /, e.g. (1|group/subgroup).

I don't think that you need to worry about autocorrelation with such a small number of time points.

Mixed Model – How to Specify Uncorrelated Random Slopes in lmer() Syntax

I think what you want is not directly achievable. The best seems to be your second option (i.e., two random intercepts but no slopes).

Depending on the number of levels in X and M, this should decrease the number of parameters overall. As in the following example:

require(lme4)

# use data with two within variables:
data(obk.long, package = "afex")

# the full model
m1 <- lmer(value ~ phase + hour + (phase + hour|id), data = obk.long)
print(m1, corr = FALSE)
# has correlations between the slopes.

# the alternative model with two intercepts:
m2 <- lmer(value ~ phase + hour + (hour|id) + (phase|id), data = obk.long)
print(m2, corr = FALSE)
# has no correlations between the slopes but two intercepts:

# m2 has overall less parameters (29 vs 36):
anova(m1, m2)

Best Answer

Related Solutions

R – Using lmer for Repeated-Measures Linear Mixed-Effect Model

Mixed Model – How to Specify Uncorrelated Random Slopes in lmer() Syntax

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