Stat 665 (Spring 2011)
Kaizar
Solutions 7
Exercises
40 points total
1. Nominal Regression
(a) The prediction equations:
log( ˆ
μ
1
/
ˆ
μ
4
)
=
0
.
13 + 0
.
79
*
A
log( ˆ
μ
2
/
ˆ
μ
4
)
=
0
.
71 + 0
.
18
*
A
log( ˆ
μ
3
/
ˆ
μ
4
)
=
0
.
19

0
.
10
*
A
Where
A
=
braceleftBigg
1
if alternating treatment
0
sequential treatment
and
μ
1
=
probability of progressive disease
μ
2
=
probability of no change
μ
3
=
probability of partial remission
μ
4
=
probability of complete remission
(b) Looking at the reported coefficients, I estimate that the odds of progressive disease (logit
= 0.79) or no change (logit = 0.18) vs. complete remission is larger for those who recieved
alternating treatment.
However, the odds of partial remission vs.
complete remission
(logit = 0.10) is smaller for those recieving alternating treatment.
Although not always necessary, it is generally a good idea to examine the other relation
ships as well:
log( ˆ
μ
1
/
ˆ
μ
3
)
=
0
.
792 + 0
.
103
=
0
.
90
log( ˆ
μ
2
/
ˆ
μ
3
)
=
0
.
176 + 0
.
103
=
0
.
28
log( ˆ
μ
1
/
ˆ
μ
2
)
=
0
.
792

0
.
176
=
0
.
61
Looking at these comparisons, I estimate that the odds of progressive disease (logit =
0.90) or no change (logit = 0.28) vs.
partial remission is greater for those receiving
alternating treatment.
Finally, the odds of progressive disease vs.
no change is also
greater for those receiving alternating treatment (logit = 0.61).
Thus, no matter how you look at it, alternating treatment seems to decrease the odds of
a successful outcome.
(c)
probability of complete remission =
e
1
e
0
.
792
+
e
0
.
176
+
e

0
.
103
+
e
1
= 0
.
387
1
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(d)
LRT
= 16
.
47901

7
.
79364 = 8
.
685
χ
2
3
(8
.
685) = 0
.
0337
Since the pvalue is so small, I conclude that the type of treatment does have a significant
association with the response.
2.
(a)
logit
(ˆ
π
1
)
=

1
.
22 + 0
.
57
A
logit
(ˆ
π
2
)
=
0
.
34 + 0
.
57
A
logit
(ˆ
π
3
)
=
1
.
38 + 0
.
57
A
Where
A
=
braceleftBigg
1
if alternating treatment
0
sequential treatment
and
π
1
=
probability of progressive disease
π
2
=
probability of progressive disease or no change
π
3
=
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 Spring '10
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 Logit, remission, progressive disease

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