Models for Count Outcomes Models for Count Outcomes

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次数依变量模型 (Models for Count Outcomes)

次数依变量模型 (Models for Count Outcomes)

Models for Count Outcomes ( 计次变量模型) Count variables indicate how many times something

Models for Count Outcomes ( 计次变量模型) Count variables indicate how many times something has happened. §美国总统否决法案的次数 §某教授发表论文的篇数 §非洲国家发生政变的次数 2

• Estimates from the linear regression models are inefficient, inconsistent, and biased –

• Estimates from the linear regression models are inefficient, inconsistent, and biased – Functional form – Nonsensical predictions 3

– A frequently adopted remedy for linear regression model is to make a natural

– A frequently adopted remedy for linear regression model is to make a natural logarithmic transformation of the dependent variable so that a log-linear function is acquired –Because zero is one of the observed values, a constantc is often added to the dependent variable. Yi, i. e. , ln(Yi +c) 4

• Example: Article Counts(论文 篇数) example (file name: couart 2): the data on

• Example: Article Counts(论文 篇数) example (file name: couart 2): the data on the number of publications produced by Ph. D. biochemists are used 5

• Count Models Poisson Regression Model (PRM泊松模型) Negative Binomial Regression Models（负二 项模型） 6

• Count Models Poisson Regression Model (PRM泊松模型) Negative Binomial Regression Models（负二 项模型） 6

• Interpretation of PRM – the expected value of the count variable (rate

• Interpretation of PRM – the expected value of the count variable (rate of occurrence): listcoef, prchange – the probability of counts: prvalue – predicted count: prtab 11

• Interpretation of PRM 1. Change in for changes in the independent variables

• Interpretation of PRM 1. Change in for changes in the independent variables – factor ( or percent) change in expected count using　 listcoef – 在其他变数固定不变的情形下, 女性 科学家的平均论文数是男性科学家的 女性科学家的0. 8倍(或, 少 20%) 12

– 在其他变数固定不变的情形下, 指 导教授的论文数增加一个标准差, 科学家的平均论文数会增加 27% For a standard deviation increase in the mentors’

– 在其他变数固定不变的情形下, 指 导教授的论文数增加一个标准差, 科学家的平均论文数会增加 27% For a standard deviation increase in the mentors’ productivity, a scientist's mean productivity increases by 27 percent, holding all other variables constant 13

– Marginal and Discrete change in (predicted rate) using prchange 在一般情形下(其他变数保持 在平均值), 女性科学家的平均 论文数会比男性少

– Marginal and Discrete change in (predicted rate) using prchange 在一般情形下(其他变数保持 在平均值), 女性科学家的平均 论文数会比男性少 0. 36篇 14

2. creating ideal types with　 prvalue and prtab: 15

2. creating ideal types with　 prvalue and prtab: 15

• Interpretation of NBM – the expected value of the count variable (rate

• Interpretation of NBM – the expected value of the count variable (rate of occurrence): listcoef, prchange – the probability of counts: prvalue – predicted count: prtab 27

• Interpretation of NBR 1. Change in for changes in the independent variables

• Interpretation of NBR 1. Change in for changes in the independent variables – factor ( or percent) change in expected count usinglistcoef 在其他变量固定不变的情形下, 女性科学家的平均论文数是男性 科学家的0. 8倍(或, 少 20%) 28

– Marginal and Discrete change in (predicted rate) usingprchange 在一般情形下(其他变量保持 在平均值), 女性科学家的平均 论文数会比男性少 0.

– Marginal and Discrete change in (predicted rate) usingprchange 在一般情形下(其他变量保持 在平均值), 女性科学家的平均 论文数会比男性少 0. 34篇 29

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