Non-parametric, multivariate, repeated measures, analysis. CLM?

Mon, Jul 8, 2013 3:23 AM

An interaction is something between covariates...not between a covariate 
and a response variable (symptoms).
More specifically...the interaction index * Time in your model tells you 
whether the relationship
between symptoms and time changes between the indices. I think what you 
are asking is whether
the main term Time is significant.

There is another problem. By concatenating all those 9 indices in one 
long vector you are introducing a new level of
dependency in your data. I assume that the first value of index 1 is 
from the same person as the first value of index 2? And the same for the 
other 7 observations.

You need to build that dependency in your model. Either with a random 
effect Participant....or in some form of GEE with a more fancy 
correlation (if you think that the correlation between the 9 indices 
differ).

Not sure if I understand where/why the non-parametric bit comes from.

Alain

I have not found a proper way to do this yet (for metric variables you
could run a simple multivariate repeated measures GLM, even SPSS can do
that in 3 clicks).

While searching for a solution I found a "trick" that I stumbled across in
Joop Hox' book "Multilevel Analysis" (second edition, 2010), pp. 189.

The trick is to reformat your long data into a long long dataset in which
you create a new DV that includes all your DV responses, and use an index
variable that holds information about the nature of the DVs to predict this
outcome.

In this dataset, I have participants * time * symptom rows. The variable
"symptoms" contains the symptom severity of participants on 9 symptoms ( 0
- 3), the variables "index" contains the information about the nature of
the symptom (1 to 9), and finally I have the variable "time".

data<-read.csv("data_long_long.csv", head=T)

data$symptoms <- factor(data$symptoms)
data$time <- factor(data$time)
data$index <-factor(data$index)

m1<-clm(symptoms ~ index*time, data = data)

  link  threshold nobs  logLik    AIC      niter max.grad cond.H
  logit flexible  26100 -20279.24 40598.47 6(0)  2.32e-12 9.1e+02

Coefficients:
                  Estimate Std. Error z value Pr(>|z|)
index2        0.23664    0.09239   2.561 0.010426 *
index3        1.18456    0.08527  13.892  < 2e-16 ***
index4        1.25951    0.08452  14.903  < 2e-16 ***
index5        0.50797    0.09022   5.630  1.8e-08 ***
index6       -0.05645    0.09716  -0.581 0.561219
index7       -0.33821    0.10261  -3.296 0.000980 ***
index8       -1.46011    0.14010 -10.422  < 2e-16 ***
index9       -1.76944    0.15673 -11.290  < 2e-16 ***
time2             1.58636    0.08392  18.904  < 2e-16 ***
index2:time2 -0.42100    0.11578  -3.636 0.000277 ***
index3:time2 -1.01586    0.11053  -9.191  < 2e-16 ***
index4:time2  0.16148    0.10865   1.486 0.137213
index5:time2 -0.09218    0.11438  -0.806 0.420298
index6:time2 -0.33049    0.12068  -2.738 0.006172 **
index7:time2 -0.25286    0.12599  -2.007 0.044749 *
index8:time2 -0.11819    0.16347  -0.723 0.469675
index9:time2 -0.66872    0.18918  -3.535 0.000408 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Threshold coefficients:
     Estimate Std. Error z value
0|1  1.52104    0.06799   22.37
1|2  3.27583    0.07102   46.13
2|3  4.86367    0.07925   61.37

Now, what I am looking for is the overall "symptom * time" interaction
term. How do I obtain this value?

Thank you
  T-

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