Between group comparison in ANOVA/Generalized Linear Model Let's ...

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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 



4.91 



4.81 



5.46 



4.93 

5.8



4.93 

5.6



4.92 

5.4



4.85 



4.99 



4.83 

4.8



4.61 

4.6



4.78 

4.4



5.26 

4.2



5.41 



5.6 



4.68 



4.59 



4.65 



4.53 



4.65 



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?