[R-sig-ME] Interpreting clmm results with ordinal effect

[Rune Haubo]

Petri,

I think you are confused about the use of orthogonal polynomials for
ordered factors in model formulas rather than cumulative link models.
If you first remove the ordering from the factors, I think you will
find the output from clmm more familiar:

df$q7_f <- factor(df$q7, ordered=FALSE)
df$sex_f <- factor(df$sex, ordered=FALSE)

It is correct, though, that the response variable, q4 should be an
ordered factor or at least a factor from which the ordering can be
inferred.

As an example consider the wine data from the ordinal package. We can
fit two models where bottle is interpreted as a factor and an ordered
factor respectively:

> library(ordinal)
Loading required package: MASS
Loading required package: ucminf
Loading required package: Matrix
Loading required package: lattice
> data(wine)
> fm1 <- clmm(rating ~ bottle + (1|judge), data=wine)
> summary(fm1)
Cumulative Link Mixed Model fitted with the Laplace approximation

formula: rating ~ bottle + (1 | judge)
data:    wine

 link  threshold nobs logLik AIC    niter    max.grad cond.H
 logit flexible  72   -80.26 184.52 21(1578) 5.23e-06 1.0e+02

Random effects:
        Var Std.Dev
judge 1.321   1.149
Number of groups:  judge 9

Coefficients:
        Estimate Std. Error z value Pr(>|z|)
bottle2   1.1992     0.9653   1.242 0.214112
bottle3   2.6116     1.0441   2.501 0.012373 *
bottle4   2.2340     1.0175   2.196 0.028126 *
bottle5   3.3366     1.0621   3.141 0.001682 **
bottle6   4.0071     1.0960   3.656 0.000256 ***
bottle7   5.9393     1.2202   4.868 1.13e-06 ***
bottle8   5.4546     1.1552   4.722 2.34e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Threshold coefficients:
    Estimate Std. Error z value
1|2  -1.0696     0.8472  -1.263
2|3   2.1406     0.8946   2.393
3|4   4.9217     1.0581   4.651
4|5   6.8276     1.1853   5.760
> wine <- transform(wine, bottle2 = factor(bottle, ordered=TRUE))
> fm2 <- clmm(rating ~ bottle2 + (1|judge), data=wine)
> summary(fm2)
Cumulative Link Mixed Model fitted with the Laplace approximation

formula: rating ~ bottle2 + (1 | judge)
data:    wine

 link  threshold nobs logLik AIC    niter    max.grad cond.H
 logit flexible  72   -80.26 184.52 19(1428) 6.90e-06 1.6e+01

Random effects:
        Var Std.Dev
judge 1.321   1.149
Number of groups:  judge 9

Coefficients:
          Estimate Std. Error z value Pr(>|z|)
bottle2.L  5.18240    0.91856   5.642 1.68e-08 ***
bottle2.Q -0.18429    0.67894  -0.271    0.786
bottle2.C  0.08646    0.66414   0.130    0.896
bottle2^4 -0.98063    0.67058  -1.462    0.144
bottle2^5 -0.65429    0.66913  -0.978    0.328
bottle2^6  0.09092    0.66348   0.137    0.891
bottle2^7 -0.63177    0.65730  -0.961    0.336
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Threshold coefficients:
    Estimate Std. Error z value
1|2  -4.1674     0.7787  -5.352
2|3  -0.9572     0.5110  -1.873
3|4   1.8239     0.5595   3.260
4|5   3.7298     0.7056   5.286

The L Q and C terms for bottle2 in fm2 denote linear, quadratic and
cubic components. In fm1 bottle has the standard treatment contrasts.
Observe that the likelihoods are identical, hence the models are
merely reparameterizations of each other.

Hope this helps,
Rune


On 14 May 2012 16:29, Petri Lankoski <petri.lankoski at gmail.com> wrote:
>
> Dear list members,
>
> I have questionnaire data (5 point likert-scale) as well as some categorical
> variable (the ordinal data is not normally distributed). I have started to
> analyze the data with ordinal package and its clmm function.  With the
> categorical data the outputs are understandable, but I have not able to
> understand the output with ordinal data (tutorials and books I have
> referenced have not been helpful). How I should interpret L, Q, C and ^4 in
> output?
>
> Cumulative Link Mixed Model fitted with the Laplace approximation
>
> formula: q4 ~ q7 + sex + (1 | game)
> data:    df
>
>  link  threshold nobs logLik  AIC     niter   max.grad cond.H
>  logit symmetric 562  -558.69 1135.37 20(857) 7.52e-06 2.8e+01
>
> Random effects:
>        Var Std.Dev
> game 0.1026  0.3204
> Number of groups:  game 11
>
> Coefficients:
>      Estimate Std. Error z value Pr(>|z|)
> q7.L    4.3726     0.3815  11.461   <2e-16 ***
> q7.Q    0.3842     0.3014   1.275   0.2024
> q7.C    0.2504     0.2504   1.000   0.3173
> q7^4    0.2771     0.2117   1.309   0.1905
> sex.L   0.2659     0.1297   2.050   0.0404 *
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Threshold coefficients:
>          Estimate Std. Error z value
> central.1  -2.5827     0.2212 -11.676
> central.2  -0.3151     0.1818  -1.733
> spacing.1   2.5340     0.1506  16.828
>
>
> Any help or pointers appreciated!
>
> --
> Petri Lankoski, petri.lankoski at iki.fi
> www.iki.fi/petri.lankoski
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

-- 
Rune Haubo Bojesen Christensen

Ph.D. Student, M.Sc. Eng.
Phone: (+45) 45 25 33 63
Mobile: (+45) 30 26 45 54

DTU Informatics, Section for Statistics
Technical University of Denmark, Build. 305, Room 122,
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