Dear all,

The post hoc Tukey p values are more significant than the initial lme found
p values. This seems weird, as multiple comparison typically results in
adjusted (lower) p values.

This is the model we fitted ('day' is ordered categorical, 'subject' a
factor, 'value' numerical):

model <- lme(fixed = value ~ day, data = data, random = ~1 | subject,
correlation = corCAR1(form = ~day | subject), na.action = na.omit)
summary( model )

Linear mixed-effects model fit by REML
 Data: subset
        AIC      BIC   logLik
  -19.37828 -8.77579 18.68914

Random effects:
 Formula: ~1 | subject
        (Intercept)   Residual
StdDev:  0.06171551 0.08085952

Correlation Structure: Continuous AR(1)
 Formula: ~day | subject
 Parameter estimate(s):
       Phi
0.06759193
Fixed effects: value ~ day
                  Value  Std.Error DF   t-value p-value
(Intercept)  0.20912634 0.04549080 20  4.597112  0.0002
day3        -0.09325478 0.04938149 20 -1.888456  0.0736
day7        -0.06965230 0.05102310 20 -1.365113  0.1874
day21       -0.08670998 0.05113215 20 -1.695801  0.1054
day49       -0.00350724 0.05113952 20 -0.068582  0.9460
day70        0.01039966 0.05114001 20  0.203357  0.8409
 Correlation:
      (Intr) day3   day7   day21  day49
day3  -0.543
day7  -0.561  0.517
day21 -0.562  0.485  0.533
day49 -0.562  0.483  0.501  0.534
day70 -0.562  0.483  0.499  0.502  0.534

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-1.85879777 -0.50415072  0.06897617  0.63312387  1.31884242

Number of Observations: 30
Number of Groups: 5
-------------------------------------------------------------------------------------------------------

Their is no significant fit for day3, day7, etc.

However, if we run a post hoc Tukey multiple comparison test, we get
significant differences between day0 and day3, day7 and day21!
How is this possible?

Thanks!

Chris Kleier

------------------------------------------------------------------------------------------------------
unique.labels <- as.numeric( unique( as.character( data$day ) ) )
K <- unique.labels
names( K ) <- paste( "day", unique.labels, sep = "" )
contrast <- contrMat( K, type = "Tukey" )
summary( glht( model, linfct = contrast ) ) )

     Simultaneous Tests for General Linear Hypotheses

Multiple Comparisons of Means: Tukey Contrasts


Fit: lme.formula(fixed = value ~ day, data = data, random = ~1 |
    subject, correlation = corCAR1(form = ~day | subject), na.action =
na.omit)

Linear Hypotheses:
                    Estimate Std. Error z value Pr(>|z|)
day3 - day0 == 0   -0.302381   0.083346  -3.628   0.0037 **
day7 - day0 == 0   -0.278779   0.085300  -3.268   0.0129 *
day21 - day0 == 0  -0.295836   0.085431  -3.463   0.0065 **
day49 - day0 == 0  -0.212634   0.085440  -2.489   0.1209
day70 - day0 == 0  -0.198727   0.085440  -2.326   0.1751
day7 - day3 == 0    0.023602   0.049381   0.478   0.9967
day21 - day3 == 0   0.006545   0.051023   0.128   1.0000
day49 - day3 == 0   0.089748   0.051132   1.755   0.4825
day70 - day3 == 0   0.103654   0.051140   2.027   0.3156
day21 - day7 == 0  -0.017058   0.049381  -0.345   0.9993
day49 - day7 == 0   0.066145   0.051023   1.296   0.7788
day70 - day7 == 0   0.080052   0.051132   1.566   0.6098
day49 - day21 == 0  0.083203   0.049381   1.685   0.5295
day70 - day21 == 0  0.097110   0.051023   1.903   0.3880
day70 - day49 == 0  0.013907   0.049381   0.282   0.9997
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported -- single-step method)

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