17DesignLME

# 17DesignLME - Experimental Designs and LME's LME models...

This preview shows pages 1–6. Sign up to view the full content.

Experimental Designs and LME’s I LME models provide one way to model correlations among observations I Very useful for experimental designs where there is more than one size of experimental unit I Or designs where the observation unit is not the same as the experimental unit. I My philosophy (widespread at ISU and elsewhere) is that the way an experiment is conducted speciﬁes the random effect structure for the analysis. I Observational studies are very different No randomization scheme, so no clearcut random effect structure Often use model selection methods to help chose the random effect structure I NOT SO for a randomized experiment. c ± 2011 Dept. Statistics (Iowa State University) Stat 511 section 17 1 / 25

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
I One example: I study designed as an RCBD. I treatments are randomly assigned within a block I analyze data, ﬁnd out block effects are small I should you delete block from the model and reanalyze? I above philosophy says “tough”. Block effects stay in the analysis I for the next study, seriously consider: blocking in a different way or using a CRD I Following pages work through details of LME’s for some common study designs c ± 2011 Dept. Statistics (Iowa State University) Stat 511 section 17 2 / 25
Mouse muscle study I Mice grouped into blocks by litter. 4 mice per block, 4 blocks. I Four treatments randomly assigned within each block I Collect two replicate muscle samples from each mouse I Measure response on each muscle sample I 16 eu., 32 ou. I Questions concern differences in mean response among the four treatments I The model usually used for a study like this is: I y ijk = μ + τ i + l j + m ij + e ijk , where y ijk is the k th measurement of the response for the mouse from litter j that received treatment i , ( i = 1 , 2 , 3 , 4 ; j = 1 , 2 , 3 , 4 ; k = 1 , 2 ) . c ± 2011 Dept. Statistics (Iowa State University) Stat 511 section 17 3 / 25

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
I The ﬁxed effects: β = μ τ 1 τ 2 τ 3 τ 4 IR 5 is an unknown vector of ﬁxed parameters I u = [ l 1 , l 2 , l 3 , l 4 , m 11 , m 21 , m 31 , m 41 , m 12 , ... , m 34 , m 44 ] 0 is a vector of random effects describing litters and mice. I ± = [ e 111 , e 112 , e 211 , e 212 , ... , e 441 , e 442 , ... , e 441 , e 442 ] 0 is a vector of random errors. I with y = [ y 111 , y 112 , y 211 , y 212 , ... , y 411 , y 412 , ... , y 441 , y 442 ] 0 , the model can be written as a linear mixed effects model y = X β + Z u + ± , where c ± 2011 Dept. Statistics (Iowa State University) Stat 511 section 17 4 / 25
X = 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 Z = 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 . . . 0 1 0 0 0 0 0 1 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 25

17DesignLME - Experimental Designs and LME's LME models...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online