Stat 665 (Spring 2011)
Kaizar
Solutions 4
Exercises
40 points total
1. Toothpaste experiment:
(a) The outcome of interest is “cavity 2”, the number of cavities after 2 years of treatment.
(b) Any of the variables gender, age, fluoride, and floss might be moderating variables if they
somehow change the relationship between the toothpaste and the number of cavities after
2 years. For example, if a patient uses mouthwash (“fluoride”), then the toothpaste may
be less effective since it would have less work to do.
(c) Cavity 1 is a potential mediating variable.
Any reduction of cavities after 1 year of
treatment is clearly a part of the overall reduction of cavities in 2 years. This variable
comes “between” the treatment and the outcome of interest.
2. Negative Binomial Regression:
(a) Random component: Negative binomial(1,
μ
)
(b) Linear component:
α
+
βX
i
(c) Link: log
3. Agresti problem 3.3
(a) Since the model is a “linear” probability model, the predition equation is: ˆ
π
= 0
.
00255 +
0
.
00109
*
Alcohol
. The intercept is the probability of a malformation if the mother drank
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 Spring '10
 Staff
 Poisson Distribution, Probability theory, Negative binomial distribution, πµ

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