Question: Prove that the Pearson residuals for the linear logit model applied to a I 2 contingency table satisfy X 2 = 1 i

Prove that the Pearson residuals for the linear logit model applied to a I × 2 contingency table satisfy X² = ∑¹_{i = 1} e²_i. Note that this holds for a binomial GL.M with any link.

Step by Step Solution

★★★★★

3.40 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We consider the contribution to the X 2 statistic of its tw... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Categorical Data Analysis Questions!

Create a logistic regression model to predict the probability of a malignant cell from the grouped radius data in Table 7.3. a. Use software to calculate the Pearson residuals. b. Create a histogram...

The form for the distribution shown in Equation (8.5) was discovered and published by Simon-Denis Poisson (17811840). One of the first applications of the Poisson distribution was in the 19th...

For the toxicity study of Table 12.9, collapsing to a binary response, consider linear logit models for the probability a fetus is normal. a. Does the ordinary binomial model show evidence of...

6.31 Prove that the Pearson residuals for the linear logit model applied to a / x 2 con- tingency table satisfy X2 = _ _e. [Hint: Start with the X sum over the 2/ cells and combine the two terms from...

2) When a GLM fits poorly according to an overall goodness-of-fit test, examination of residuals highlights where the fit is poor. The Pearson residual for observation i is Yi - ei = Prove that the...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Running head: SEXUAL EDUCATION MODELS IN THE UNITED STATES Sexual Education Models in the United States and their Impact on Sexual Attitudes and Behaviors DePaul University 1 SEXUAL EDUCATION MODELS...

STAB22H3 Statistics I 2020 1.A researcher used a linear regression model to investigate the relationship between sexually transmitted disease rate (y) and poverty rate (x) in the U.S.A. The...

Article review on journal of The Role of Micro and Small Business Enterprises in Linking Youth and Women in to Business: A Case Study in South Gondar Zone, Ethiopia Dejen Debeb Asmare1Alebel Weretaw...

Residents of Green Acres, a gated community located in the City of Foothills, voted to form a local improvement district to fund the construction of a neighborhood park. The city agreed to administer...

General Electric likes to manipulate earnings by buying companies and incorporating the acquired earnings into it's financial results. Half way through the fourth quarter it realizes it needs to...

Credit & Cashflow Metrics FY Dec FY2021A FY2022A FY2023A FY2024F FY2025F Debt / Equity Net Debt / Equity Debt / Assets Net Debt / Assets EBITDA / Int Exp Debt / EBITDA ST Debt / Total Debt (*) [Cash...

Of the 1,395 colleges in the United States, 364 have 2-year schools. In a random sample of 40 two-year schools, it was found that the text Statistics Can Be Fun was used in 10 of the schools. In an...

Larry Bird, who played pro basketball for the Boston Celtics, was known for being a good shooter. In games during 19801982, when he missed his first free throw, 48 out of 53 times he made the second...

An article 4 in www.networkworld.com about evaluating e-mail filters that are designed to detect spam described a test of Mail Frontiers Anti-Spam Gateway (ASG). In the test, there were 7840 spam...

Johnson Enterprises Inc. is involved in the manufacture and sale of electronic components used in small AM/FM radios. The firm needs $300,000 to finance an anticipated expansion in receivables due to...

Assume the Black-Scholes framework. You are given the following information about two stocks X and Y: ALess than 2 B: At least 2 but less than 4 C: At least 4 but less than 6 D: At least 6 but less...

A put option on a stock with a current price of $37 has an exercise price of $39. The price of the corresponding call option is $2.85. According to put-call parity, if the effective annual risk-free...