Between group comparison in ANOVA/Generalized Linear Model. Let's say, we have a dataset with multilevel treatment and a continuous response variables:.
Between group comparison in ANOVA/Generalized Linear Model Let's say, we have a dataset with multilevel treatment and a continuous response variables: treatment response 7
4.83
7
4.91
7
4.81
6
5.46
6
4.93
5.8
6
4.93
5.6
5
4.92
5.4
5
4.85
5
4.99
4
4.83
4.8
4
4.61
4.6
4
4.78
4.4
3
5.26
4.2
3
5.41
3
5.6
2
4.68
2
4.59
2
4.65
1
4.53
1
4.65
1
4.66
treatment Weighted Marginal Means Wald X²(7)=107.08, p=0.0000 6.2
response
6.0
5.2 5.0
4.0 1
2
3
4
5
6
7
treatment
1. We run ANOVA in GLZ module with sigma‐restricted parameterization (STATISTICA or SPSS); treatment 7 is the reference group. The results are: response - Parameter estimates (example) Distribution : NORMAL Link function: LOG Level of - Effect Estimate Standard - Error Wald - Stat.
p
Intercept
1.587607 0.005364
87599.79
0.000000
treatment 1
-0.058656 0.013772
18.14
0.000021
treatment 2
-0.052892 0.013704
14.90
0.000114
treatment 3
0.103104 0.012049
73.22
0.000000
treatment 4
-0.031570 0.013460
5.50
0.019005
treatment 5
0.005702 0.013047
0.19
0.662096
treatment 6
0.042940 0.012652
11.52
0.000689
0.119921 0.018504
42.00
0.000000
Scale
Problem: When looking in the observed means, very few of these treatment effects (the difference from the reference) makes sense.
2. When no sigma‐restricted parameterization is used, the results are more realistic, but still not quite: response - Parameter estimates (example) Distribution : NORMAL Link function: LOG Level of - Effect Estimate Standard - Error Wald - Stat.
p
Intercept
1.578979 0.014276
12234.03
0.000000
treatment 1
-0.050028 0.020713
5.83
0.015722
treatment 2
-0.044264 0.020651
4.59
0.032073
treatment 3
0.111732 0.019151
34.04
0.000000
treatment 4
-0.022942 0.020424
1.26
0.261330
treatment 5
0.014330 0.020046
0.51
0.474693
treatment 6
0.051568 0.019688
6.86
0.008811
treatment 7
0.000000 42.00
0.000000
0.119921 0.018504
Scale
3. Changing LOG link to IDENTITY does not have much effect. 4. When the same data are analyzed with ANOVA module, with Dunnett’s post hoc test and treatment 7 as a control group, the results are: Dunnett test; variable response (example) Probabilities for Post Hoc Tests (2-sided) Error: Between MS = .02157, df = 14.000 treatment
{7} 4.8500
1
1
0.254232
2
2
0.354544
3
3
0.001481
4
4
0.862988
5
5
0.978479
6
6
0.194778
7
7
My question is ‐ how the between‐group comparison is done for categorical multilevel variables in Generalized Linear Models module?
