comparing 3 levels of fixed factor in lme4
Well, you can use the t-statistics for comparison-wise tests! the issue is whether one ought to do this, or whether one should do some kind of overall test. As I see it, all depends on the purpose that is in mind. As Professor Dalgaard says, the issue is much the same as for lm models. You can for example do:
library(DAAG) a1 <- lme(ShootDryMass ~ fert+variety, random=~1|Block, data=rice) anova(a1)
numDF denDF F-value p-value (Intercept) 1 67 72.39 <.0001 fert 2 67 3.94 0.0241 variety 1 67 25.48 <.0001 As the design is balanced, the order of terms does not affect the anova F-test. But as the design is balanced, you be better to do:
rice.aov <- aov(ShootDryMass ~ fert+variety+Error(Block), data=rice) summary(rice.aov)
Error: Block
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 1 3528 3528
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
fert 2 7019 3509 3.94 0.024
variety 1 22685 22685 25.48 3.7e-06
Residuals 67 59657 890
John Maindonald email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473 fax : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm
On 30/07/2012, at 9:38 PM, Obermeier Andrew wrote:
Thank you John Maindonald. For more than 2 levels of the experimental condition, I learned that usually we find an F to test mean differences across the levels of the condition. In lme4, the model summary reports a t value, and I am replicating a study that uses lme4 to compare 3 levels of a fixed factor. My advising professor has told me that the t value can only be used to compare 2 means. Andrew Obermeier On Jul 30, 2012, at 8:00 PM, John Maindonald <john.maindonald at anu.edu.au> wrote:
Perhaps Andrew has vaguely at the back of his mind the notion that for comparing >2 means, one should be using a multiple range test or an anova test, at all events if the aim is to achieve an experiment-wise 5% level. Tests based on the individual t-statistics are not independent. This is of course a somewhat controversial area. John Maindonald email: john.maindonald at anu.edu.au phone : +61 2 (6125)3473 fax : +61 2(6125)5549 Centre for Mathematics & Its Applications, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200. http://www.maths.anu.edu.au/~johnm On 30/07/2012, at 8:38 PM, peter dalgaard wrote:
On Jul 30, 2012, at 08:04 , Obermeier Andrew wrote:
In lme4, in models with 3 levels of the fixed factor, each of these gets a t value comparing it to a reference level. How is this done? It is my understanding that the t value can only be used to compare 2 means.
Then your understanding is wrong, and you need to read a text on basic linear modelling theory. Nothing specifically mixed-model or even R relevant about that. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
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