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q82b, q82d and q82f. Similarly, bcc
j
, bbc
j
, and bj
j
are used to denote the slopes associated
with different countries, business codes and job titles. The 'bounds' and 'lincon' statements
(lines 15-21) jointly specify the monotone constraints associated with the intercept
parameters and the slopes of the customer satisfaction covariates. Lines 22-29 define the log
likelihood for each customer which, for the
i
-th customer, is given by
5
loglik (
,
)
YPYj
log
(
)
i
ij
i
j
1
Covariate
MLE of Slope
Covariate
MLE of Slope
Unconstrained
Constrained
Unconstrained
Constrained
1.92
2.01
1.27
1.27
q
79a
q
82d
1
1
q
79a
2.09
2.01
q
82d
.92
.96
2
2
q
79a
1.43
1.43
q
82d
.67
.73
3
3
q
79a
.84
.82
q
82d
.77
.73
4
4
q
79a
.58
.57
q
82d
.44
.42
5
5
.19
.19
.19
.19
q
79a
q
82d
6
6
q
79a
Structural 0
Implied 0
q
82d
Structural 0
Implied 0
7
7
2.68
2.56
.85
1.28
q
82a
q
82f
1
1
q
82a
.71
.98
q
82f
1.69
1.28
2
2
1.05
.98
1.08
1.07
q
82a
q
82f
3
3
q
82a
.89
.88
q
82f
.69
.69
4
4
.31
.30
.59
.58
q
82a
q
82f
5
5
q
82a
.14
.14
q
82f
.16
.16
6
6
q
82a
Structural 0
Implied 0
q
82f
Structural 0
Implied 0
7
7
q
82b
1.31
1.28
1
q
82b
.81
.85
2
.75
.77
q
82b
3
q
82b
.53
.56
4
.14
.21
q
82b
5
q
82b
.23
.21
6
q
82b
Structural 0
Implied 0
7
Table 5. Unconstrained and Constrained Slope MLEs of Customer Satisfaction Covariates
Table 5 provides a side-by-side comparison of the constrained and unconstrained MLEs for
the slopes of the customer satisfaction covariates, and Figure 2 is a plot that shows the
monotone behavior of the constrained estimates. There is very little difference between the
unconstrained and constrained MLEs for the demographic covariates. Recall that for the
unconstrained MLEs, the zero for the slope of the last level of each covariate is a structural
zero resulting from the non-full rank dummy variable coding used when fitting the model.
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