This script is Example 3 from the SAS© documentation for PROC NLMIXED. It analyzes inhaler data (Ezzet and Whitehead, 1991) by fitting a proportional odds model with random effects. It defines bounds for threshold parameters and uses the `probnorm` function to manually construct the log-likelihood function.
Data Analysis
Type : CREATION_INTERNE
The 'inhaler' data is created via a DATA step with DATALINES. The original syntax suggests using ' @@' to read multiple observations per line.
1 Code Block
DATA STEP Data
Explanation :
Creation of the 'inhaler' dataset. The INPUT statement uses the ' @@' modifier to read data continuously (multiple observations per physical line). Variables 'gt' (interaction) and 'sub' (subject identifier) are calculated.
Creation of the 'inhaler' dataset. The INPUT statement uses the ' @@' modifier to read data continuously (multiple observations per physical line). Variables 'gt' (interaction) and 'sub' (subject identifier) are calculated.
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| 1 | DATA inhaler; |
| 2 | INPUT clarity group time freq @@; |
| 3 | gt = group*time; |
| 4 | sub = floor((_n_+1)/2); |
| 5 | DATALINES; |
| 6 | 1 0 0 59 1 0 1 59 1 0 0 35 2 0 1 35 1 0 0 3 3 0 1 3 1 0 0 2 |
| 7 | 4 0 1 2 2 0 0 11 1 0 1 11 2 0 0 27 2 0 1 27 2 0 0 2 3 0 1 2 |
| 8 | 2 0 0 1 4 0 1 1 4 0 0 1 1 0 1 1 4 0 0 1 2 0 1 1 1 1 0 63 |
| 9 | 1 1 1 63 1 1 0 13 2 1 1 13 2 1 0 40 1 1 1 40 2 1 0 15 2 1 1 15 |
| 10 | 3 1 0 7 1 1 1 7 3 1 0 2 2 1 1 2 3 1 0 1 3 1 1 1 4 1 0 2 |
| 11 | 1 1 1 2 4 1 0 1 3 1 1 1 |
| 12 | ; |
2 Code Block
PROC NLMIXED
Explanation :
Estimation of the nonlinear mixed model. The 'general' distribution is used to specify a custom log-likelihood ('ll') based on the cumulative normal distribution function (probnorm). The model includes a random effect 'u' normally distributed at the subject level 'sub'. 'REPLICATE' accounts for the frequency variable.
Estimation of the nonlinear mixed model. The 'general' distribution is used to specify a custom log-likelihood ('ll') based on the cumulative normal distribution function (probnorm). The model includes a random effect 'u' normally distributed at the subject level 'sub'. 'REPLICATE' accounts for the frequency variable.
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| 1 | PROC NLMIXED DATA=inhaler corr ecorr; |
| 2 | parms b0=0 b1=0 b2=0 b3=0 sd=1 i1=1 i2=1; |
| 3 | bounds i1 > 0, i2 > 0; |
| 4 | eta = b0 + b1*group + b2*time + b3*gt + u; |
| 5 | IF (clarity=1) THEN p = probnorm(-eta); |
| 6 | ELSE IF (clarity=2) THEN |
| 7 | p = probnorm(i1-eta) - probnorm(-eta); |
| 8 | ELSE IF (clarity=3) THEN |
| 9 | p = probnorm(i1+i2-eta) - probnorm(i1-eta); |
| 10 | ELSE p = 1 - probnorm(i1+i2-eta); |
| 11 | IF (p > 1e-8) THEN ll = log(p); |
| 12 | ELSE ll = -1e20; |
| 13 | model clarity ~ general(ll); |
| 14 | random u ~ normal(0,sd*sd) subject=sub; |
| 15 | replicate freq; |
| 16 | estimate 'thresh2' i1; |
| 17 | estimate 'thresh3' i1 + i2; |
| 18 | estimate 'icc' sd*sd/(1+sd*sd); |
| 19 | RUN; |
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