时间效应内重复测量方差分析治疗的事后统计分析

Question

I am having trouble finding a post hoc test to decipher at what "Session" or time I have a treatment within session affect.

This is my data:

TR  SESSION MAC FISHD      ID
1   1      1    3.285714286 1
2   1      2    0.571428571 2
2   1      3    3.571428571 3
1   1      4    4           4
1   2      1    4           5
2   2      2    6.571428571 6
2   2      3    3.142857143 7
1   2      4    8.857142857 8
1   3      1    0.714285714 9
2   3      2    1.714285714 10
2   3      3    4.428571429 11
1   3      4    0.714285714 12

This is how I got repeated measures:

model.b = lme(FISHD ~ TR + SESSION + TR*SESSION, 
            random = ~1|MAC,
            data=TTDall2)

> ACF(model.b)
  lag        ACF
1   0  1.0000000
2   1 -0.7547232
3   2  0.4852727

> model2 = lme(FISHD ~ TR + SESSION + TR*SESSION, 
+ random = ~1|MAC,
+ correlation = corAR1(form = ~ SESSION | MAC,
+                                                                                                                                               value = -0.7547232),
+   data=TTDall2,
+  method="REML")
> Anova(model2)
Analysis of Deviance Table (Type II tests)

Response: FISHD
                     Chisq      Df Pr(>Chisq)    
TR               0.2014     1     0.6536    
SESSION          25.0418    1   5.61e-07 ***
TR:SESSION       103.9113   1  < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

I am trying to decipher when there is a treatment affect. Any ideas?

Answer 1

At the moment you are modeling session as a continuous variable and so the reported coefficient for TR:SESSION is sort of a "test of trend" across the range 1:3 for that value of SESSION in TRT=2 .... is that what you were hoping to discover? Let's do it the right way, with factors and in particular create an ordered factor:

model2 = lme(FISHD ~ factor(TR)*ordered(SESSION), # same as TRT+SESSION+TRT*ORDERED
 random = ~1|MAC,
 correlation = corAR1(form = ~ SESSION | MAC,
 value = -0.7547232),
   data=dat,
  method="REML")
 anova(model2)
 #------
                            numDF denDF  F-value p-value
(Intercept)                     1     4 37.48966  0.0036
factor(TR)                      1     2  0.20124  0.6976
ordered(SESSION)                2     4 13.94379  0.0157
factor(TR):ordered(SESSION)     2     4 52.02864  0.0014

So this is saying that an analysis that takes into account the interaction of TRT with sequence of SESSIONs finds a significant difference for the effect of TRT. If you do not model the interaction (using formula: FISHD ~ factor(TR)+ordered(SESSION) , then neither component is significant:

model1 = lme(FISHD ~  factor(TR)+ordered(SESSION), 
 random = ~1|MAC,
 correlation = corAR1(form = ~ SESSION | MAC, value = -0.7547232),
   data=dat,
  method="REML")
 anova(model1)
 #-------------
                 numDF denDF  F-value p-value
(Intercept)          1     6 44.53272  0.0005
factor(TR)           1     2  0.14143  0.7430
ordered(SESSION)     2     6  2.55154  0.1578

And:

>  anova(model1, model2)
       Model df      AIC      BIC    logLik   Test  L.Ratio p-value
model1     1  7 54.74813 55.30422 -20.37406                        
model2     2  9 44.04435 42.17018 -13.02217 1 vs 2 14.70378   6e-04
Warning message:
In anova.lme(model1, model2) :
  fitted objects with different fixed effects. REML comparisons are not meaningful.

That is a warning but I do not think it applies here since the varaialbes in the model are the same and only the structure is different.