A study is conducted to investigate the association between income level and political party affilia- tion in the USA. Income level has 5 levels: Lowest (lowest 20-th percentile), low, middle, high, and very high (top 20-th percentile). Political party has 3 categories: Democratic (D), Independent (I), and Republican (R). A baseline category logit multinomial is fit on the 3 response categories using covariate of income level as ordinal (with scores 1, 2, 3, 4, and 5 for the categories lowest, low, middle, high and very high respectively). Base category of response is Independent. The fitted model is log(îp/î¹) = 3.3 – 0.2x and log(FR/Î1) = 1.0 +0.3x, where x=1,2,3,4,5 (poverty levels as numeric/ordinal), π is the probability of being Democrat, TI is the probability of being Independent, and TR is the probability of being Republican. a. Comparing the chances/probability of being Republican to Independent, interpret the effect of income level increases on the odds (of being Republican versus being Independent, Republican is the numerator). b. For what income levels is R > ₁ (probability of being Republican is greater than probability of being Independent) ?
A study is conducted to investigate the association between income level and political party affilia- tion in the USA. Income level has 5 levels: Lowest (lowest 20-th percentile), low, middle, high, and very high (top 20-th percentile). Political party has 3 categories: Democratic (D), Independent (I), and Republican (R). A baseline category logit multinomial is fit on the 3 response categories using covariate of income level as ordinal (with scores 1, 2, 3, 4, and 5 for the categories lowest, low, middle, high and very high respectively). Base category of response is Independent. The fitted model is log(îp/î¹) = 3.3 – 0.2x and log(FR/Î1) = 1.0 +0.3x, where x=1,2,3,4,5 (poverty levels as numeric/ordinal), π is the probability of being Democrat, TI is the probability of being Independent, and TR is the probability of being Republican. a. Comparing the chances/probability of being Republican to Independent, interpret the effect of income level increases on the odds (of being Republican versus being Independent, Republican is the numerator). b. For what income levels is R > ₁ (probability of being Republican is greater than probability of being Independent) ?
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A study is conducted to investigate the association between income level and political party affiliation in the USA. Income level has 5 levels: Lowest (lowest 20-th percentile), low, middle, high, and
very high (top 20-th percentile).
Political party has 3 categories: Democratic (D), Independent (I), and Republican (R).
A baseline category logit multinomial is fit on the 3 response categories using covariate of income
level as ordinal (with scores 1, 2, 3, 4, and 5 for the categories lowest, low, middle, high and very
high respectively). Base category of response is Independent.
The fitted model is log(ˆπD/πˆI ) = 3.3 − 0.2x and log(ˆπR/πˆI ) = 1.0 + 0.3x,
where x=1,2,3,4,5 (poverty levels as numeric/ordinal), πD is the probability of being Democrat, πI
is the probability of being Independent, and πR is the probability of being Republican.
a. Comparing the chances/probability of being Republican to Independent, interpret the effect of
income level increases on the odds (of being Republican versus being Independent, Republican is
the numerator).
b. For what income levels is πˆR > πˆI (probability of being Republican is greater than probability
of being Independent) ?
Transcribed Image Text:A study is conducted to investigate the association between income level and political party affilia-
tion in the USA. Income level has 5 levels: Lowest (lowest 20-th percentile), low, middle, high, and
very high (top 20-th percentile).
Political party has 3 categories: Democratic (D), Independent (I), and Republican (R).
A baseline category logit multinomial is fit on the 3 response categories using covariate of income
level as ordinal (with scores 1, 2, 3, 4, and 5 for the categories lowest, low, middle, high and very
high respectively). Base category of response is Independent.
1.0+ 0.3x,
The fitted model is log(^D/1) = 3.3 - 0.2x and log(^R/^I)
where x=1,2,3,4,5 (poverty levels as numeric/ordinal), π is the probability of being Democrat, TI
is the probability of being Independent, and is the probability of being Republican.
=
a. Comparing the chances/probability of being Republican to Independent, interpret the effect of
income level increases on the odds (of being Republican versus being Independent, Republican is
the numerator).
b. For what income levels is îR > ÎI (probability of being Republican is greater than probability
of being Independent) ?
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