[R-sig-ME] Hierarchical modelling using lmer v lme and including weights

Tue Sep 13 00:10:55 CEST 2011

Dear Mailing List

Earlier last week I posted a question on R-help 'Power analysis in hierarchical models' requesting guidance on power analysis, using a simulation approach.  Many thanks to Thierry Onkelinx for his useful suggestions which included submitting such requests to this, more appropriate, forum.  

I am stepping backward now in attempting to best model the pilot data that I have.  These data (243 x 4) are appended below this email and I apologise in advance if this is an inappropriate method of getting data out.  To get the data into R copy them to the clipboard prior to running the attached script.  My questions are in the script behind #

I'd be glad to receive any sources of information* on the subject of analysis of hierarchical models (i.e. book recommendations) or websites.  

Many thanks for your help (and patience). 

Tom. 
* Crawley, The R Book, Page 649 demonstrates recoding factor levels prior to constructing the lmer model (for nested rat liver data, cross ref:  Sokal and Rohlf, Biometry (3rd ed), page 291).  Anyone know why it is necessary to recode, the factors as per Crawley ?  Using the model Glycogen~Treatment+(1|rat)+(1|liver) (as per Crawley) seems to indicate that there are six rats whilst using the 'alternative' Glycogen~Treatment+(1|Rat/Liver) seems to indicate (correctly) that there are two rats.  

============================================================

library(psych);  library(lme4);  library(nlme)

data4=read.clipboard(sep='\t')
data4$Treat=factor(data4$Treat)#  Treat is a factor
str(data4)  #LogG =response,Treat=fixed effect, Tank and Pot=random. Several measurements of LogG were made in each pot, there were several pots in each Tank.  

with (data4, tapply(LogG,list(Tank,Treat),mean));# show some data structure
with (data4, tapply(LogG,list(Pot,Treat),mean));# as above.

# I AM INTERESTED IN THE RESPONSE (LOGG) TO DIFFERENT LEVELS OF TREAT. 
# THE TANKS REPRESENT THE TRUE REPLICATES IN THIS EXPERIMENTS 

#Q1 - CAN I GET P VALUES? (Treat0.1 - looks 'significant' (P<0.05) but only just

#check residuals: 
Res1=residuals(model_1,type=n);  plot(Res1~Treat,data=data4)

#model_1 shows difference variances for different levels of Treat, try varIdent
vf1=varIdent(form=~1|Treat)
model_2=lmer(LogG~Treat+(1|Tank)+(1|Pot), weights=vf1, data=data4);summary(model_2)#OR
model_2=lmer(LogG~Treat+(1|Tank/Pot), weights=vf1, data=data4);summary(model_2)
# Q2 - model_2 fails, why the error message - '...variable lengths differ'?

#Different approach 
#USE lme 
model_3=lme(LogG~Treat,random=~1|Tank+1|Pot,weights=vf1,data=data4); summary(model_3)
#Q3 - Model_3 'runs' but get error message '....+ not meaningful for factors'. Why?

#respecify random component - looks more encouraging:
model_3=lme(LogG~Treat,random=~1|Tank/Pot,weights=vf1,data=data4);  summary(model_3)
#Q3.1 - Should I assume from these results that the variances components indicate that most of the variance is occurring at the residual level 
# i.e. the level of individual measurements within each pot and that, therefore, I could usefully additionally replicate these measurements?

#Q3.2 can I get appropriate degrees of freedom with the parameter estimates (for fixed effects)?  This would reassure that correct analysis is being conducted?

====================
RAW DATA (copy the headers)

Tank	Treat	Pot	LogG
Tank 1	0.1	A	3.258096538
Tank 1	0.1	A	3.044522438
Tank 1	0.1	A	4.262679877
Tank 1	0.1	A	3.33220451
Tank 1	0.1	A	1.791759469
Tank 1	0.1	A	1.386294361
Tank 1	0.1	B	4.430816799
Tank 1	0.1	B	4.890349128
Tank 1	0.1	B	4.584967479
Tank 1	0.1	B	5.225746674
Tank 1	0.1	B	3.871201011
Tank 1	0.1	B	2.302585093
Tank 1	0.1	B	1.945910149
Tank 1	0.1	C	3.044522438
Tank 1	0.1	C	5.398162702
Tank 1	0.1	C	0
Tank 1	0.1	C	2.890371758
Tank 1	0.1	C	3.761200116
Tank 1	0.1	C	3.713572067
Tank 1	0.1	C	4.406719247
Tank 1	0.1	D	4.143134726
Tank 1	0.1	D	4.709530201
Tank 1	0.1	D	2.564949357
Tank 1	0.1	D	3.871201011
Tank 1	0.1	D	4.672828834
Tank 1	0.1	D	4.48863637
Tank 1	0.1	D	4.094344562
Tank 2	0.02	A	3.33220451
Tank 2	0.02	A	2.708050201
Tank 2	0.02	A	3.17805383
Tank 2	0.02	A	3.401197382
Tank 2	0.02	A	2.564949357
Tank 2	0.02	A	1.386294361
Tank 2	0.02	A	4.48863637
Tank 2	0.02	B	4.025351691
Tank 2	0.02	B	4.369447852
Tank 2	0.02	B	2.63905733
Tank 2	0.02	B	3.433987204
Tank 2	0.02	B	3.401197382
Tank 2	0.02	B	3.33220451
Tank 2	0.02	C	1.609437912
Tank 2	0.02	C	2.890371758
Tank 2	0.02	C	3.17805383
Tank 2	0.02	C	4.143134726
Tank 2	0.02	C	3.044522438
Tank 2	0.02	C	3.135494216
Tank 2	0.02	C	2.63905733
Tank 2	0.02	D	2.197224577
Tank 2	0.02	D	2.397895273
Tank 2	0.02	D	2.995732274
Tank 2	0.02	D	3.828641396
Tank 2	0.02	E	1.386294361
Tank 2	0.02	E	2.995732274
Tank 2	0.02	E	3.258096538
Tank 2	0.02	E	3.17805383
Tank 2	0.02	E	4.262679877
Tank 2	0.02	E	3.610917913
Tank 2	0.02	E	2.890371758
Tank 2	0.02	E	3.465735903
Tank 2	0.02	F	3.044522438
Tank 2	0.02	F	5.298317367
Tank 2	0.02	F	2.890371758
Tank 2	0.02	F	3.850147602
Tank 2	0.02	F	3.091042453
Tank 2	0.02	F	3.761200116
Tank 2	0.02	F	4.204692619
Tank 3	0.1	A	3.80666249
Tank 3	0.1	A	3.465735903
Tank 3	0.1	A	4.276666119
Tank 3	0.1	A	2.708050201
Tank 3	0.1	A	5.587248658
Tank 3	0.1	A	2.48490665
Tank 3	0.1	A	4.276666119
Tank 3	0.1	B	2.890371758
Tank 3	0.1	B	2.564949357
Tank 3	0.1	B	3.135494216
Tank 3	0.1	B	2.197224577
Tank 3	0.1	C	5.837730447
Tank 3	0.1	C	1.609437912
Tank 3	0.1	C	4.96284463
Tank 3	0.1	C	5.384495063
Tank 3	0.1	C	4.317488114
Tank 3	0.1	D	4.317488114
Tank 3	0.1	D	3.988984047
Tank 3	0.1	D	2.48490665
Tank 3	0.1	D	4.663439094
Tank 3	0.1	D	2.48490665
Tank 3	0.1	D	4.304065093
Tank 3	0.1	D	1.609437912
Tank 4	0	A	2.63905733
Tank 4	0	A	1.791759469
Tank 4	0	A	3.044522438
Tank 4	0	A	3.33220451
Tank 4	0	A	2.833213344
Tank 4	0	A	0
Tank 4	0	A	2.890371758
Tank 4	0	A	3.496507561
Tank 4	0	B	3.433987204
Tank 4	0	B	3.044522438
Tank 4	0	B	3.135494216
Tank 4	0	B	2.63905733
Tank 4	0	B	2.772588722
Tank 4	0	B	3.610917913
Tank 4	0	C	3.713572067
Tank 4	0	C	2.197224577
Tank 4	0	C	4.394449155
Tank 4	0	C	3.433987204
Tank 4	0	C	3.17805383
Tank 4	0	C	2.564949357
Tank 4	0	C	2.995732274
Tank 4	0	C	2.302585093
Tank 4	0	D	3.688879454
Tank 4	0	D	3.737669618
Tank 4	0	D	2.833213344
Tank 4	0	D	2.564949357
Tank 4	0	D	3.044522438
Tank 4	0	D	3.401197382
Tank 4	0	D	3.401197382
Tank 5	0.02	A	4.382026635
Tank 5	0.02	A	4.025351691
Tank 5	0.02	A	4.262679877
Tank 5	0.02	A	4.043051268
Tank 5	0.02	A	3.465735903
Tank 5	0.02	A	3.044522438
Tank 5	0.02	A	3.17805383
Tank 5	0.02	B	3.091042453
Tank 5	0.02	B	4.709530201
Tank 5	0.02	B	4.127134385
Tank 5	0.02	B	3.970291914
Tank 5	0.02	B	3.80666249
Tank 5	0.02	B	2.197224577
Tank 5	0.02	B	2.48490665
Tank 5	0.02	C	2.944438979
Tank 5	0.02	C	2.302585093
Tank 5	0.02	C	3.555348061
Tank 5	0.02	C	3.33220451
Tank 5	0.02	C	3.465735903
Tank 5	0.02	C	2.63905733
Tank 5	0.02	C	3.555348061
Tank 5	0.02	D	2.708050201
Tank 5	0.02	D	3.218875825
Tank 5	0.02	D	3.33220451
Tank 5	0.02	D	3.044522438
Tank 5	0.02	D	3.496507561
Tank 5	0.02	D	1.609437912
Tank 5	0.02	D	3.33220451
Tank 5	0.02	E	3.610917913
Tank 5	0.02	E	2.772588722
Tank 5	0.02	E	2.772588722
Tank 5	0.02	E	3.465735903
Tank 5	0.02	E	2.63905733
Tank 5	0.02	E	3.17805383
Tank 5	0.02	F	3.465735903
Tank 5	0.02	F	1.945910149
Tank 5	0.02	F	3.737669618
Tank 5	0.02	F	2.995732274
Tank 5	0.02	F	3.951243719
Tank 5	0.02	F	2.772588722
Tank 5	0.02	F	1.098612289
Tank 6	0.1	A	4.521788577
Tank 6	0.1	A	1.609437912
Tank 6	0.1	A	4.418840608
Tank 6	0.1	A	3.218875825
Tank 6	0.1	A	3.218875825
Tank 6	0.1	A	4.787491743
Tank 6	0.1	B	1.791759469
Tank 6	0.1	B	4.718498871
Tank 6	0.1	B	4.248495242
Tank 6	0.1	B	2.63905733
Tank 6	0.1	B	3.36729583
Tank 6	0.1	B	5.030437921
Tank 6	0.1	B	2.302585093
Tank 6	0.1	C	4.9698133
Tank 6	0.1	C	2.772588722
Tank 6	0.1	C	3.688879454
Tank 6	0.1	C	4.382026635
Tank 6	0.1	C	2.564949357
Tank 6	0.1	C	3.465735903
Tank 6	0.1	C	4.304065093
Tank 6	0.1	C	4.584967479
Tank 6	0.1	D	2.944438979
Tank 6	0.1	D	3.871201011
Tank 6	0.1	D	4.290459441
Tank 6	0.1	D	4.454347296
Tank 6	0.1	D	5.451038454
Tank 6	0.1	D	3.583518938
Tank 7	0	A	4.110873864
Tank 7	0	A	3.871201011
Tank 7	0	A	3.555348061
Tank 7	0	A	3.688879454
Tank 7	0	A	3.988984047
Tank 7	0	A	4.189654742
Tank 7	0	A	5.087596335
Tank 7	0	A	3.091042453
Tank 7	0	B	3.871201011
Tank 7	0	B	3.610917913
Tank 7	0	B	2.890371758
Tank 7	0	B	2.772588722
Tank 7	0	B	3.091042453
Tank 7	0	B	4.219507705
Tank 7	0	B	4.262679877
Tank 7	0	B	3.871201011
Tank 7	0	C	3.583518938
Tank 7	0	C	2.995732274
Tank 7	0	C	1.386294361
Tank 7	0	C	2.944438979
Tank 7	0	C	2.995732274
Tank 7	0	C	3.761200116
Tank 7	0	C	3.610917913
Tank 7	0	C	3.850147602
Tank 7	0	D	3.17805383
Tank 7	0	D	4.025351691
Tank 7	0	D	3.970291914
Tank 7	0	D	3.555348061
Tank 7	0	D	3.663561646
Tank 7	0	D	4.343805422
Tank 7	0	D	4.219507705
Tank 7	0	D	3.33220451
Tank 8	0	A	2.079441542
Tank 8	0	A	3.63758616
Tank 8	0	A	4.59511985
Tank 8	0	A	4.234106505
Tank 8	0	B	2.995732274
Tank 8	0	B	3.258096538
Tank 8	0	B	3.091042453
Tank 8	0	B	1.609437912
Tank 8	0	B	2.197224577
Tank 8	0	B	4.17438727
Tank 8	0	B	3.583518938
Tank 8	0	B	4.532599493
Tank 8	0	C	3.555348061
Tank 8	0	C	2.890371758
Tank 8	0	C	2.48490665
Tank 8	0	C	3.135494216
Tank 8	0	C	3.688879454
Tank 8	0	C	2.890371758
Tank 8	0	C	3.258096538
Tank 8	0	D	3.258096538
Tank 8	0	D	3.17805383
Tank 8	0	D	2.079441542
Tank 8	0	D	2.63905733
Tank 8	0	D	3.401197382
Tank 8	0	E	3.17805383

-------------------------------------------------------------------------
Tom Wilding, MSc, PhD, Dip. Stat.
Scottish Association for Marine Science,
Scottish Marine Institute,
OBAN
Argyll.  PA37 1QA
United Kingdom.
Phone (+44) (0) 1631 559214
Fax (+44) (0) 1631 559001
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