# [R-sig-ME] Power Analysis for Linear Mixed Model with Covariates

Ulf Köther ukoether at uke.de
Wed May 14 00:41:24 CEST 2014

```Dear Gerasimos,

I am really no expert, but I would guess, you get no slope because you
implemented time as a factor variable, therefore lmer is giving you
correlated random intercepts, one for each factor-level...
Just try to add another variable for time:

expdat <- expand.grid(kid = factor(1:500), Time = factor(1:4), Treat = c("XTx", "BAU"))
expdat\$obs <- factor(seq(nrow(expdat)))
expdat\$time.month <- rep(c(0,3,6,9), each = 500)

...

fit1 <- lmer(Outcome ~ Treat*Time + (1 + time.month | kid), data = expdat)

This should give you what you want, I think...

Ulf

Am 14.05.2014 00:12, schrieb Gerasimos Fergadiotis:
> I would like to conduct a power analysis for a linear mixed model with fixed effects for Treatment(two levels) and Time (four time points: pre, mid, post treatment, 3 months post treatment; each three months apart) and correlated random effects for children (intercepts and slopes). I am using the following code in R using the lmer function:
>
> expdat <- expand.grid(kid = factor(1:500), Time = factor(1:4), Treat = c("XTx", "BAU"))
> expdat\$obs <- factor(seq(nrow(expdat)))
> set.seed(101)
> nsim <- 20
> beta <- c(100, -7, 8, 15, 20, 0, 0, 0)
> theta <- c(15.000000, 7.500000, 7.500000, 7.500000, 12.990381, 4.330127, 4.330127,
>            12.247449, 3.061862, 11.858541)
> ss <- simulate(~Treat*Time + (1+Time | kid), nsim = nsim, family = gaussian,
>       weights = rep(25, nrow(expdat)), newdata = expdat, newparams =
>       list(theta = theta, beta = beta, sigma = 1))
> expdat\$Outcome <- ss[, 1]
> fit1 <- lmer(Outcome ~ Treat*Time + (1+Time | kid), data = expdat)
> I have the following questions:
>
> In the output I see the variance associated with the random intercepts at each time point and their correlation. However, I cannot find in the output the variance associated with the slopes, and I cannot find information about the correction between the intercepts and the slopes. Where is that information?
> How does the lmer know that Time has levels and that it should estimate a unique effect for each level of the Time factor instead of a general slope parameter?
> I am attaching the summary statement of the model:
> Linear mixed model fit by REML ['lmerMod']
> Formula: Outcome ~ Treat * Time + (1 + Time | kid)
> Data: expdat
>
> REML criterion at convergence: 22951.8
>
> Scaled residuals:
> Min       1Q   Median       3Q      Max
> -2.55473 -0.47186 -0.00007  0.47268  2.57786
>
> Random effects:
> Groups   Name        Variance Std.Dev. Corr
>  kid      (Intercept) 235.4531 15.3445
>           Time2       230.9249 15.1962  0.43
>           Time3       220.6076 14.8529  0.52 0.53
>           Time4       213.2725 14.6039  0.48 0.51 0.52
>  Residual               0.9749  0.9874
> Number of obs: 4000, groups: kid, 500
>
> Fixed effects:
>                 Estimate Std. Error t value
> (Intercept)    100.92006    0.68765  146.76
> TreatBAU        -6.94796    0.06245 -111.26
> Time2            7.39371    0.68246   10.83
> Time3           15.17849    0.66717   22.75
> Time4           19.27623    0.65608   29.38
> TreatBAU:Time2  -0.16052    0.08831   -1.82
> TreatBAU:Time3  -0.05291    0.08831   -0.60
> TreatBAU:Time4  -0.14215    0.08831   -1.61
>
> Correlation of Fixed Effects:
>             (Intr) TrtBAU Time2  Time3  Time4  TBAU:T2 TBAU:T3
> TreatBAU    -0.045
> Time2        0.422  0.046
> Time3        0.510  0.047  0.528
> Time4        0.468  0.048  0.506  0.520
> TretBAU:Tm2  0.032 -0.707 -0.065 -0.033 -0.034
> TretBAU:Tm3  0.032 -0.707 -0.032 -0.066 -0.034  0.500
> TretBAU:Tm4  0.032 -0.707 -0.032 -0.033 -0.067  0.500   0.500
>
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Dipl.-Psych. Ulf Köther

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Klinik für Psychiatrie und Psychotherapie
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