Non-parametric, multivariate, repeated measures analysis. CLM?
On Jul 7, 2013, at 13:16 , Torvon wrote:
Dear all, I need to run a non-parametric, multivariate, repeated measures analysis. I have 9 ordered DVs (depression symptoms) on a scale between 0 and 3, and 2 measurement points.
Ahem. There is nothing nonparametric about these models. You have to be very much aware of the (parametric) assumptions that are being made.
What I want to find out is whether there is an interaction between time * symptoms, that is, whether symptoms differ in their change over time. 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).
Again, "simple" and "multivariate repeated" do not go well together. Do you use an unspecified covariance, or a compound symmetry one? With or without epsilon corrections. 3 clicks may get you one of them, but are you sure you understand all implications?
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
Shouldn't there be a (random) effect of participant somewhere? I.e. a clmm() model? Possibly also random interactions between participant:time and participant:symptoms.
Now, what I am looking for is the overall "symptom * time" interaction term. How do I obtain this value?
If you have the correct error model (and enough participants), it should be a matter of comparing the model with deterministic part index*time to the one with index+time. Presumably, anova() is your friend.
Thank you T- [[alternative HTML version deleted]]
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