Solved – Mean center the dependent variable for within-subject comparison

mixed modelrepeated measures

I am doing a mixed model using the different subjects as a random effect. For avoiding any between-subject comparison I am mean-centering the different explanatory variables. Is it correct to also mean-center the dependent variable? I do not find any reason not to do it, but I have not find any paper doing it.

Thank you

Best Answer

There is no reason to center the dependent variable. All this will achieve is to change the estimate for the global intercept (fixed effect). All the other estimates will remain unchanged. If you do center it, then you will need to add the value of the mean to get predictions on the original scale.

For example:

require(lme4)
m0 <- lmer(weight ~ Time * Diet + (1 + Time | Chick), data=ChickWeight, REML=F)
summary(m0)

m1 <- lmer(weight - mean(ChickWeight$weight) ~ Time * Diet + (1 + Time | Chick), data=ChickWeight, REML=F)
summary(m1)

Formula: weight ~ Time * Diet + (1 + Time | Chick)
   Data: ChickWeight

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Chick    (Intercept) 103.61   10.179        
          Time         10.01    3.165   -0.99
 Residual             163.36   12.781        
Number of obs: 578, groups:  Chick, 50

Fixed effects:
           Estimate Std. Error t value
(Intercept)  33.6541     2.8023  12.009
Time          6.2799     0.7303   8.598
Diet2        -5.0205     4.8072  -1.044
Diet3       -15.4038     4.8072  -3.204
Diet4        -1.7475     4.8145  -0.363
Time:Diet2    2.3293     1.2508   1.862
Time:Diet3    5.1430     1.2508   4.112
Time:Diet4    3.2528     1.2515   2.599

Formula: weight - mean(ChickWeight$weight) ~ Time * Diet + (1 + Time | Chick)
   Data: ChickWeight

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Chick    (Intercept) 103.61   10.179        
          Time         10.01    3.165   -0.99
 Residual             163.36   12.781        
Number of obs: 578, groups:  Chick, 50

Fixed effects:
            Estimate Std. Error t value
(Intercept) -88.1642     2.8023 -31.461
Time          6.2799     0.7304   8.598
Diet2        -5.0205     4.8072  -1.044
Diet3       -15.4038     4.8072  -3.204
Diet4        -1.7475     4.8145  -0.363
Time:Diet2    2.3293     1.2508   1.862
Time:Diet3    5.1430     1.2508   4.112
Time:Diet4    3.2528     1.2515   2.599

Related Solutions

Solved – Is balanced data assumption necessary for linear mixed effect model for repeated measurement

There are two separate topics here: Firstly, what should one do about missing longitudinal data. Secondly, what does the particular model do and what are the assumptions behind that.

Let's start with the second one. Random effects models (whether done using lmer or PROC MIXED in SAS or some other software) can automatically handle missing data for you when there is a random subject effect, because that random subject effect together with any fixed model effects allows you to predict the missing values. This is something the model implicitly does and take into account. This happens under the assumption that the missing data are missing at random (MAR). This means that there are no unobserved data that explain the missingness (e.g. it would be fine, if subjects decide to quit the study based on the data you have observed, but not if they do it due to the value you would have observed, but did not). What a standard random effects model for repeated measures does also assumes that the future values would occur under the same conditions (e.g. if subjects were taking some treatment, then for the missing values that get implicitly imputed it is assumed that they continue on this treatment).

Regarding the first topic:

Deleting all subjects with some missing data ("listwise deletion") is only valid under an assumption of missing completely at random (MCAR), which is an incredibly strong assumptions that is hardly ever applicable (usually only when data are missing, because some data got lost, not when it is due to something that happened to the subject under observation). In short, it is hardly ever the right thing to do.
Doing something that is valid under MAR (e.g. mixed models for repeated measures, multiple imputation of some form etc.): It is more often plausible that the missing data mechanism results in data being MAR, but as explained above, you may or may not be interested in the question that will be answered (the estimand). One major difficulty is that while you can check from the data whether MCAR may apply or not, you cannot really tell whether when MCAR does not apply you can assume MAR or not. Any analysis approach that is valid under MAR is also valid under MCAR, but analyses that are valid for MCAR (such as listwise deletion) are not typically valid under MAR.
Making some missing not at random (MNAR) assumptions: There is a huge number of missing data mechanisms that full into this category (everything that is not MAR or MCAR).

Whether you assume MAR or MNAR also partially depends on what question you try to answer, something that is for example currently being discussed in great detail for drug trials with a planned addendum to the guideline on statistical principles for clinical trials and with lots of journal discussions e.g. here, here and here. One useful webpage is http://www.missingdata.org.uk/.

Solved – Controlling for continuous variable in linear-mixed-effect model

Turning my comments into an answer.

To estimate the parameters you're interested in, there's no need to fit models, extract residuals and run new models. It's easier and better to specify all of the terms together in one model:

#Using lme4 instead of nlme here because I'm more familiar with the syntax
library(lme4)
lmer(V5 ~ V4 * V7 + V6 + V2 + (1|V1))

However, based on your questions I would recommend that you read more about linear models (and mixed models in particular) so you understand exactly what each of those parameters is doing. For example, your question about age and subject ID is hard to answer unless we know more about subject ID. I've assumed that individual subjects were measured multiple times; if so, the model above should work well (though you could consider whether random slopes are also needed). If individuals were measured only once, then you don't need a random effect at all and the model would simply be:

lm(V5 ~ V4 * V7 + V6 + V2)

Perhaps more importantly, this is assuming no nonlinearity in the effect of any of the continuous parameters. If there are such nonlinearities, you will need to modify the model.

Best Answer

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Solved – Is balanced data assumption necessary for linear mixed effect model for repeated measurement

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