[R-sig-ME] Linear Mixed-Effects Models (lme), question about parameter estimates and random effect
Paul Johnson
pauljohn32 at gmail.com
Wed Nov 18 06:25:07 CET 2009
On Mon, Nov 9, 2009 at 1:01 AM, R.S. Cotter <cotter.rs at gmail.com> wrote:
> Hello,
>
> I have a question regarding Linear Mixed-Effects Models (lme). I have
> searched help forum, but find it difficult to find an answer on my question.
> Probaly there is an easy answer to this, but due to lack of knowledge I can
> not understand following :
>
I had to read this a few times before I got it. Maybe others struggle as well.
Can I try to re-state it?
The data matrix looks like this, where two outcome variables,
FeedingTime and FeedingWithPrep are the same for group a, but differ
for group b.
Diet FeedingTime FeedingWithPrep
a 2 2
a 3 3
a 1 1
b 4 5
b 5 7
b 3 4
You note that linear models fitted to these 2 outcome variables have
the same estimates for group a (the intercept and Gramm), which makes
sense because the group a data is unchanged. The estimates including b
are different.
But the mixed model, which includes a random effect for the place, is
different. The estimates for group a are altered, even though the
dependent variable is the same in either case.
If that's the question, I think the answer is that the random place
effect "ranges across" both groups a and b, so it is only natural that
the estimates for both groups would be affected. Place is apparently
not completely independent of diet in the realization of the sample,
so the intercept and the estimate for Gram are affected slightly.
But I'm not completely certain of that answer. But I'm pretty sure
that's your question. :)
Maybe the folks who actually know the answer will speak up on this.
HTH
pj
> I look at whether there is a difference in the effect of weight (gram)
> between two diets ("a" and "b") on feeding time. Place is random effect (5
> different locations). I ran script 1a), so far so good. I get the intercept
> and slope for diet "a" and "b". But for diet "b" I also want to add extra
> time needed for preparing (only diet "b" needs preparing). Feeding time for
> diet "a" is the same, only feeding time for diet "b" increases. I ran script
> 1b), as expect intercept and slope for diet "b" changes, but why does
> intercept and slope for diet "a" change? The feeding time is equal for
> diet "a" in both script 1a) and 1b). Then I tried to see what happens when
> not control for random effect by using lm, and ran script 2a) and 2b). And
> now the intercept and slope for diet "a" is the same for both script
> (without and with preparing time for diet "b"). Could the difference be a
> result of how the random effect is being calculated for in lme? The
> difference is minimal, but I would like to understand why the intercept and
> slope for diet "a" changes?
>
> Sorry if my question is too simple.
>
> Regards Cotter
>
> 1a)
>> lmefit1<-lme(log10(FeedingTime) ~
> log10(Gram)*Diet,random=~1|Place,data=diet)
> 1b)
>> lmefit2<-lme(log10(FeedingtimeWithPrep) ~
> log10(Gram)*Diet,random=~1|Place,data=diet)
>> summary(lmefit1)
> Linear mixed-effects model fit by REML
> Data: diet
> AIC BIC logLik
> -24.12282 -19.12354 18.06141
> Random effects:
> Formula: ~1 | Place
> (Intercept) Residual
> StdDev: 0.0505571 0.07350342
> Fixed effects: log10(FeedingTime) ~ log10(Gram) * Diet
> Value Std.Error DF t-value p-value
> (Intercept) 0.3111653 0.3737451 13 0.832560 0.4201
> log10(Gram) 1.1664078 0.2735981 13 4.263216 0.0009
> Dietb 1.1580016 0.5148035 13 2.249405 0.0425
> log10(Gram):Dietb -0.6904469 0.3321850 13 -2.078501 0.0580
> Correlation:
> (Intr) lg10(G) Dietb
> log10(Gram) -0.996
> Dietb -0.740 0.726
> log10(Gram):Dietb 0.833 -0.826 -0.985
> Standardized Within-Group Residuals:
> Min Q1 Med Q3 Max
> -2.2608248 -0.3226060 -0.1256394 0.5658181 1.6808270
> Number of Observations: 21
> Number of Groups: 5
>
>> summary(lmefit2)
> Linear mixed-effects model fit by REML
> Data: diet
> AIC BIC logLik
> -29.98107 -24.98179 20.99054
> Random effects:
> Formula: ~1 | Place
> (Intercept) Residual
> StdDev: 0.03568998 0.06341113
> Fixed effects: log10(FeedingtimeWithPrep) ~ log10(Gram) * Diet
> Value Std.Error DF t-value p-value
> (Intercept) 0.3001162 0.3210428 13 0.934817 0.3669
> log10(Gram) 1.1760924 0.2352253 13 4.999855 0.0002
> Dietb 1.0937006 0.4302214 13 2.542181 0.0246
> log10(Gram):Dietb -0.5178826 0.2805392 13 -1.846026 0.0878
> Correlation:
> (Intr) lg10(G) Dietb
> log10(Gram) -0.996
> Dietb -0.757 0.746
> log10(Gram):Dietb 0.845 -0.840 -0.986
> Standardized Within-Group Residuals:
> Min Q1 Med Q3 Max
> -2.94950911 -0.19998787 -0.11069540 0.09370866 1.65930147
> Number of Observations: 21
> Number of Groups: 5
>
>
> 2a)
>> lmfit1<-lm(log10(FeedingTime) ~ log10(Gram)*Diet,data=diet)
> 2b)
>> lmfit2<-lm(log10(FeedingtimeWithPrep) ~ log10(Gram)*Diet,data=diet)
>> summary(lmfit1)
> Call:
> lm(formula = log10(FeedingTime) ~ log10(Gram) * Diet, data = diet)
> Residuals:
> Min 1Q Median 3Q Max
> -0.23163 -0.03347 0.01312 0.05164 0.12056
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 0.2942 0.4297 0.685 0.50277
> log10(Gram) 1.1833 0.3156 3.750 0.00160 **
> Dietb 1.1472 0.5302 2.164 0.04501 *
> log10(Gram):Dietb -0.6922 0.3578 -1.935 0.06983 .
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Residual standard error: 0.08699 on 17 degrees of freedom
> Multiple R-squared: 0.901, Adjusted R-squared: 0.8836
> F-statistic: 51.59 on 3 and 17 DF, p-value: 9.492e-09
> 2b)
>> summary(lmfit2)
> Call:
> lm(formula = log10(FeedingtimeWithPrep) ~ log10(Gram) * Diet,
> data = diet)
> Residuals:
> Min 1Q Median 3Q Max
> -0.2316266 -0.0003216 0.0001792 0.0058846 0.1205559
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 0.2942 0.3512 0.838 0.413840
> log10(Gram) 1.1833 0.2579 4.588 0.000262 ***
> Dietb 1.0359 0.4333 2.391 0.028665 *
> log10(Gram):Dietb -0.4902 0.2924 -1.676 0.112005
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Residual standard error: 0.0711 on 17 degrees of freedom
> Multiple R-squared: 0.9698, Adjusted R-squared: 0.9645
> F-statistic: 182 on 3 and 17 DF, p-value: 4.069e-13
>
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--
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas
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