Matthew Wolak
2011-Jul-21 03:29 UTC
[R] gls yields much smaller std. errors with different base for contrasts
Dear List,
After running a compound symmetric model using gls, I realized that
the default contrasts were not the ones that made the most sense given
the biological relationships among the factor levels. When I either
changed the factor levels to re-arrange the order they occur in the
gls model (not shown below) OR specifically change the contrasts I get
the exact same estimates for the intercepts but now with TINY standard
errors for these estimates. Below is some example code and output for
what I am attempting.
1>
rep<-as.factor(c(1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2))
1>
tank<-as.factor(c(2,2,2,2,2,2,7,7,7,7,7,7,1,1,1,3,3,3,6,6,6,8,8,8,4,4,4,4,4,4,5,5,5,5,5,5))
1>
sex_ratio<-as.factor(c("6m:6f","6m:6f","6m:6f","6m:6f","6m:6f","6m:6f","6m:6f","6m:6f","6m:6f",
1+
"6m:6f","6m:6f","6m:6f","3m:9f","3m:9f","3m:9f","3m:9f","3m:9f","3m:9f","3m:9f","3m:9f",
1+
"3m:9f","3m:9f","3m:9f","3m:9f","6m:0f","6m:0f","6m:0f","6m:0f","6m:0f","6m:0f","6m:0f",
1+
"6m:0f","6m:0f","6m:0f","6m:0f","6m:0f"))
1>
response<-c(62.62,72.25,68.88,81.31,54.82,81.60,100.54,66.17,120.74,109.64,79.23,65.84,
1+
81.49,99.81,93.39,85.42,157.41,32.92,97.8,49.17,53.42,76.30,74.72,24.84,131.83,113.64,
1+ 103,152.05,118.94,65.71,133.98,106.40, 108.57,156.37,110.66,126.76)
1> tmp.data<-data.frame(rep, tank, sex_ratio, response)
1> str(tmp.data)
'data.frame': 36 obs. of 4 variables:
$ rep : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 2 2 2
2 ...
$ tank : Factor w/ 8 levels
"1","2","3","4",..: 2 2 2 2 2 2 7 7 7 7
...
$ sex_ratio: Factor w/ 3 levels "3m:9f","6m:0f",..: 3 3 3 3
3 3 3 3 3 3 ...
$ response : num 62.6 72.2 68.9 81.3 54.8 ...
1> ###Now the first model
1> library(nlme)
1> cs1<-gls(response~rep * sex_ratio, data=tmp.data,
1+ corr=corCompSymm(, form=~ 1 | tank), method="ML")
1> summary(cs1)
Generalized least squares fit by maximum likelihood
Model: response ~ rep * sex_ratio
Data: tmp.data
AIC BIC logLik
223.8389 236.5071 -103.9195
Correlation Structure: Compound symmetry
Formula: ~1 | tank
Parameter estimate(s):
Rho
-0.2
Coefficients:
Value Std.Error t-value p-value
(Intercept) 91.74000 7.589296 12.088077 0.0000
rep2 -29.03167 10.732886 -2.704926 0.0112
sex_ratio6m:0f 22.45500 7.589296 2.958772 0.0060
sex_ratio6m:6f -21.49333 7.589296 -2.832059 0.0082
rep2:sex_ratio6m:0f 38.62667 10.732886 3.598908 0.0011
rep2:sex_ratio6m:6f 49.14500 10.732886 4.578918 0.0001
Correlation:
(Intr) rep2 sx_6:0 sx_6:6 r2:_6:0
rep2 -0.707
sex_ratio6m:0f -1.000 0.707
sex_ratio6m:6f -1.000 0.707 1.000
rep2:sex_ratio6m:0f 0.707 -1.000 -0.707 -0.707
rep2:sex_ratio6m:6f 0.707 -1.000 -0.707 -0.707 1.000
Standardized residuals:
Min Q1 Med Q3 Max
-2.6848135 -0.6039727 0.0249904 0.5257303 2.9974788
Residual standard error: 21.90841
Degrees of freedom: 36 total; 30 residual
1> levels(tmp.data$sex_ratio)
[1] "3m:9f" "6m:0f" "6m:6f"
1> #Now change the contrasts so the base level is the all male sex
ratio (i.e., 6m:0f)
1> tmp.data$sex_ratiob<-tmp.data$sex_ratio
1> contrasts(tmp.data$sex_ratio) #original contrasts
6m:0f 6m:6f
3m:9f 0 0
6m:0f 1 0
6m:6f 0 1
1> #Set new contrasts for the copied sex_ratio column (i.e.,
"sex_ratiob")
1>
contrasts(tmp.data$sex_ratiob)<-contr.treatment(n=levels(tmp.data$sex_ratio),
base=2, contrasts=TRUE)
1> contrasts(tmp.data$sex_ratiob) #new contrasts
3m:9f 6m:6f
3m:9f 1 0
6m:0f 0 0
6m:6f 0 1
1> ##Now try the model again
1> cs2<-gls(response~rep * sex_ratiob, data=tmp.data,
1+ corr=corCompSymm(, form=~ 1 | tank), method="ML")
1> summary(cs2)
Generalized least squares fit by maximum likelihood
Model: response ~ rep * sex_ratiob
Data: tmp.data
AIC BIC logLik
223.8389 236.5071 -103.9195
Correlation Structure: Compound symmetry
Formula: ~1 | tank
Parameter estimate(s):
Rho
-0.2
Coefficients:
Value Std.Error t-value p-value
(Intercept) 114.19500 0.000003 36429283 0.0000
rep2 9.59500 0.000004 2164380 0.0000
sex_ratiob3m:9f -22.45500 7.589296 -3 0.0060
sex_ratiob6m:6f -43.94833 0.000004 -9913590 0.0000
rep2:sex_ratiob3m:9f -38.62667 10.732886 -4 0.0011
rep2:sex_ratiob6m:6f 10.51833 0.000006 1677724 0.0000
Correlation:
(Intr) rep2 sx_3:9 sx_6:6 r2:_3:
rep2 -0.707
sex_ratiob3m:9f 0.000 0.000
sex_ratiob6m:6f -0.707 0.500 0.000
rep2:sex_ratiob3m:9f 0.000 0.000 -0.707 0.000
rep2:sex_ratiob6m:6f 0.500 -0.707 0.000 -0.707 0.000
Standardized residuals:
Min Q1 Med Q3 Max
-2.6848135 -0.6039727 0.0249904 0.5257303 2.9974788
Residual standard error: 21.90841
Degrees of freedom: 36 total; 30 residual
1> #The intercepts of the sex_ratios are the same
1> coefficients(summary(cs1))[1] #3m:9f intercept in cs1
(Intercept)
91.74
1> coefficients(summary(cs2))[1]+coefficients(summary(cs2))[3] #3m:9f
intercept in cs2
(Intercept)
91.74
1> coefficients(summary(cs1))[1]+coefficients(summary(cs1))[3] #6m:0f
intercept in cs1
(Intercept)
114.195
1> coefficients(summary(cs2))[1] #6m:0f intercept in cs2
(Intercept)
114.195
1> coefficients(summary(cs1))[1]+coefficients(summary(cs1))[4] #6m:6f
intercetp in cs1
(Intercept)
70.24667
1> coefficients(summary(cs2))[1]+coefficients(summary(cs2))[4] #6m:6f
intercetp in cs2
(Intercept)
70.24667
#Curiously, removing the interaction [gls(response~rep +
sex_ratiob...)] gives reasonable numbers for the standard errors
Any suggestions would be greatly appreciated! Thank you.
Sincerely,
Matthew
--
Matthew Wolak
PhD Candidate
Evolution, Ecology, and Organismal Biology Graduate Program
University of California Riverside
http://student.ucr.edu/~mwola001/
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