# [R] GLM and POST HOC test INTERPRETATION

CHIRIBOGA Xavier xavier.chiriboga at unine.ch
Thu Feb 9 01:08:39 CET 2017

```Dear colleagues,

I am analyzing a data set of 68 values (integers). In some treatments (exactly 6) the values are "zero". Because I record 0 in my measurement (or really a small value below zero)

My experiment is designed in such a way that I record values for 6 treatments at 2 times. Replicates are different in each combination time-treatment.

I am running a GLM , poisson distribution, for ANOVA I used Chisq, and for the POST HOC test I used Tukey.

I try to detect if interaction is significant, so I build the script:    expresion~time*treatment

Effects of time, treatment are interaction are significant. However, when I run the script for Tukey comparisons, I only get 15 comparisons. Of course I cannot interpret that:

these comparisons are the same for Time 1 and Time 2, since there is a significant effect of time. Moreover, I got a warning message : covariate interactions found. I dont know if I am doing right? I dont know what to do?

Xavier

PhD Student

University of Neuchatel

lm3=glm(expresion~time*treatment,family="poisson")
> summary(lm3)

Call:
glm(formula = expresion ~ time * treatment, family = "poisson")

Deviance Residuals:
Min       1Q   Median       3Q      Max
-5.3796  -1.4523  -0.6642   1.2277   6.3909

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)            2.09964    0.29508   7.115 1.12e-12 ***
time                   0.20294    0.19255   1.054 0.291895
treatmentCHA0+Db      -0.17004    0.36180  -0.470 0.638356
treatmentDb            1.68952    0.37624   4.490 7.11e-06 ***
treatmentHEALTHY       0.84035    0.50340   1.669 0.095049 .
treatmentPCL           0.32072    0.37950   0.845 0.398041
treatmentPCL+Db        0.54365    0.34047   1.597 0.110320
time:treatmentCHA0+Db  0.87314    0.22626   3.859 0.000114 ***
time:treatmentDb      -0.82803    0.26539  -3.120 0.001808 **
time:treatmentHEALTHY -1.36987    0.38318  -3.575 0.000350 ***
time:treatmentPCL      0.08474    0.24635   0.344 0.730851
time:treatmentPCL+Db   0.39244    0.21521   1.824 0.068217 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 1173.05  on 66  degrees of freedom
Residual deviance:  403.07  on 55  degrees of freedom
AIC: 707.95

Number of Fisher Scoring iterations: 5

> anova(lm3,test="Chisq")
Analysis of Deviance Table

Response: expresion

Terms added sequentially (first to last)

Df Deviance Resid. Df Resid. Dev  Pr(>Chi)
NULL                              66    1173.05
time            1   100.55        65    1072.50 < 2.2e-16 ***
treatment       5   561.69        60     510.81 < 2.2e-16 ***
time:treatment  5   107.75        55     403.07 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> summary(glht(lm3, mcp(treatment="Tukey")))

Simultaneous Tests for General Linear Hypotheses

Multiple Comparisons of Means: Tukey Contrasts

Fit: glm(formula = expresion ~ time * treatment, family = "poisson")

Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
CHA0+Db - CHA0 == 0     -0.1700     0.3618  -0.470   0.9970
Db - CHA0 == 0           1.6895     0.3762   4.490   <0.001 ***
HEALTHY - CHA0 == 0      0.8404     0.5034   1.669   0.5402
PCL - CHA0 == 0          0.3207     0.3795   0.845   0.9568
PCL+Db - CHA0 == 0       0.5437     0.3405   1.597   0.5892
Db - CHA0+Db == 0        1.8596     0.3135   5.931   <0.001 ***
HEALTHY - CHA0+Db == 0   1.0104     0.4584   2.204   0.2266
PCL - CHA0+Db == 0       0.4908     0.3174   1.546   0.6231
PCL+Db - CHA0+Db == 0    0.7137     0.2696   2.648   0.0817 .
HEALTHY - Db == 0       -0.8492     0.4699  -1.807   0.4491
PCL - Db == 0           -1.3688     0.3338  -4.101   <0.001 ***
PCL+Db - Db == 0        -1.1459     0.2887  -3.969   <0.001 ***
PCL - HEALTHY == 0      -0.5196     0.4725  -1.100   0.8764
PCL+Db - HEALTHY == 0   -0.2967     0.4418  -0.672   0.9842
PCL+Db - PCL == 0        0.2229     0.2929   0.761   0.9725
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)

Warning message:
In mcp2matrix(model, linfct = linfct) :
covariate interactions found -- default contrast might be inappropriate

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