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# How to test regression forms? - Glimmix with significant interactions and heterogeneous error

[ Edited ]

Hi,

I've run a RCBD with one categorical fixed effect (peptide, 7 levels) and one quantitative effect (peptide concentration, 5 levels). Using distribution=lognormal link=identity I almost met normality based on my Shapiro-Wilk statistic, and otherwise all my plots of residuals looked fine. By modelling a covariance structure for heterogeneous error over concentration, I was able to meet all assumptions.

SAS Output

Class Level Information Class Levels Values block peptide conc
 4 1 2 3 4 7 A B Control D E F G 5 6.25 12.5 25 50 100

My analysis of variance showed a significant peptide*conc interaction. Now I am wanting to test the significance of linear, quadratic and lack of fit regressions for concentration over each level of peptide. My textbook, 'A hitchhiker's guide to statistics in biology', provides two methods for doing this. One is through the 'dummy variable method', however this method cannot be applied if covariance structures for heterogeneous error are used. The other method is through contrast statements, however I cannot figure out how to do this over each level of peptide separately. Please help! How can I go abouts this?

Thanks for the help, I know it can take time to respond to these questions and I'm very grateful if you are willing. Please note that I am rather novice at SAS in your explanations of how to proceed.

Cheers.

Here is my code for analysis of variance:

``````Proc glimmix data=final;
class block peptide conc;
model fluo= peptide|conc / distribution=lognormal link=identity ddfm=kr;
random block;
random _residual_ / subject=block*peptide*conc group=conc;
covtest homogeneity / est restart;
ods output contrasts=b;
ods output lsmeans=backtr;
output out=second predicted=pred student=studentresid residual(noblup)=mresid student(noblup)=smresid residual=resid;
contrast 'BP100 linear'
estimate 'CPPs vs Control Peptide' peptide 1 1 -6 1 1 1 1 / divisor=6;
estimate 'mean of control' intercept 1 peptide 0 0 1 0 0 0 0 / divisor=1;
estimate 'mean of CPPs' intercept 6 peptide 1 1 0 1 1 1 1 / divisor=6;
estimate 'fusion peptides vs conventional CPPs' peptide -1 1 0 -1 1 1 -1 / divisor=3;
estimate 'mean of fusion peptides' intercept 3 peptide 0 1 0 0 1 1 0 / divisor=3;
estimate 'mean of conventional CPPs' intercept 3 peptide 1 0 0 1 0 0 1 / divisor=3;
lsmestimate peptide 'mean of BP100' 1 0 0 0 0 0 0, 'mean of BP1002k*' 0 1 0 0 0 0 0, 'mean of CONTROL' 0 0 1 0 0 0 0, 'mean of R9' 0 0 0 1 0 0 0, 'mean of R9BP100' 0 0 0 0 1 0 0, 'mean of R9TAT2' 0 0 0 0 0 1 0, 'mean of TAT2' 0 0 0 0 0 0 1 / divisor=7;
lsmeans peptide*conc;
covtest 'likelihood ratio test if block=0' 0 . . . . . . / est restart;
run;``````

SAS Output

` `
```Type III Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
peptide 6 82.27 381.99 <.0001
conc 4 47.9 1431.10 <.0001
peptide*conc 24 66.91 9.62 <.0001 ```
```Estimates
Label Estimate Standard
Error DF t Value Pr > |t|
CPPs vs Control Peptide 1.4707 0.05779 82.27 25.45 <.0001
mean of control 5.5614 0.09318 5.904 59.68 <.0001
mean of CPPs 7.0321 0.07935 3.121 88.62 <.0001
fusion peptides vs conventional CPPs 1.5947 0.04368 82.27 36.51 <.0001
mean of fusion peptides 7.8295 0.08230 3.612 95.13 <.0001
mean of conventional CPPs 6.2347 0.08230 3.612 75.75 <.0001

```
```Contrasts
Label Num DF Den DF F Value Pr > F
peptides*conc linear among fusion peptides 2 56.52 3.55 0.0354
peptides*conc quadratic among fusion peptides 2 70.89 0.57 0.5671
peptides*conc lack of fit among fusion peptides 4 45.41 0.84 0.5089
peptides*conc linear among conventional CPPs 2 56.52 18.45 <.0001
peptides*conc quadratic among conventional CPPs 2 70.89 0.87 0.4242
peptides*conc lack of fit among conventional CPPs 4 45.41 0.86 0.4923
peptides*conc linear among all 6 56.52 33.90 <.0001
peptide*conc quadratic among all 6 70.89 4.45 0.0007
peptide*conc lack of fit among all 2 40.88 48.80 <.0001 ```
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