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Interpreting clmm results with ordinal effect

2 messages · Petri Lankoski, Rune Haubo

Original
Petri Lankoski
# 
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!
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:
Loading required package: MASS
Loading required package: ucminf
Loading required package: Matrix
Loading required package: lattice
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
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: