Question: Refer to logit model (6.4) for a 2 2 K contingency table {n ijk }. a. Using dummy variables, write the log-likelihood function.

Refer to logit model (6.4) for a 2 × 2 × K contingency table {n_ijk}.

a. Using dummy variables, write the log-likelihood function. Identify the sufficient statistics for the various parameters. Explain how to conduct exact conditional inference about the effect of X, controlling for Z.

b. Using a basic result for testing in exponential families, explain why uniformly most powerful unbiased tests of conditional XY independence are based on ∑_k n_11k.

Step by Step Solution

★★★★★

3.33 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The loglikelihood function for the logit model for a 2 2 K contingency table can be written as log L k i j nijk logpijk 1 pijk k i j nijk xijk where ... 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!

The log likelihood function for the linear regression model with normally distributed disturbances is shown in Example 4.6. Show that at the maximum likelihood estimators of b for and e'e/n for 2 ,...

Write the log likelihood L for model (XZ, YZ). Calculate L/ and show that it implies +++ = n. Show that L/ i X = n i++ i++ . Similarly, differentiate with respect to each parameter to obtain...

For testing independence in a contingency table of size r Ã c, the degrees of freedom (df) for the chi-squared distribution equal df = (r - 1) Ã (c - 1). They have the following...

Create charts to better understand data sets. For cross-sectional data, use a scatter chart. For time series data, use a line chart. Linear y = a + bx Logarithmic y = ln(x) Polynomial (2nd order) y =...

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...

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)....

1 2 3 4 7 8 9 12 13 14 15 16 17 18 19 20 21 22 23 24 28 29 30 31 38 40 41 44 47 48 49 50 51 62 63 64 66 67 68 69 70 71 73 74 76 77 78 79 80 81 82 85 86 87 88 89 90 91 92 93 94 95 99 100 101 104 105...

** You can use EXCEL or any other software. ** You need to include your printout in your submissions. The layout and format of the paper should include the following sections: Title page, Abstract,...

Investigate the social media use, in as many vehicles as possible, of a favourite brand, and asses which social media appears most effective for that brand.

Show that the differential equation of Exercise 6.30 with b = c = 0 and Ï > 0 yields a normal distribution. In exercise 1 dlf(x)] a +bx + cx? fx) dx

The partially completed inventory record for the rotor subassembly in the table below shows gross requirements, scheduled receipts, lead time, and current on-hand inventory. a. Complete the last...

How is the role of the ventromedial prefrontal cortex and orbitofrontal cortex similar for value decisions and social behavior? ________________________________________

Sketch a scatter plot for which r > 0, but r = 0 after one of the points is deleted.

Refer to the previous exercise. The correlation with the cost of a dinner is 0.68 for food quality rating, 0.69 for service rating, and 0.56 for dcor rating. According to the definition of r 2 as a...

For the 32 nations in Example 7, we found a correlation of 0.614 between Internet use and Facebook use (both as percentages of population). The regression equation is predicted Facebook use = 7.90 +...

Debt Crisis With the creation of the European Monetary System and the birth of the euro in 1999, the U.S dollar is facing challenges to its position as the key reserve currency in international...

How many payments will it take for your bank account to grow to $ 5 0 0 0 if you deposit $ 2 0 0 at the end of each month and the account earns 9 % compounded monthly? a 1 8 payments b 1 0 payments c...

Assume that the following three stocks, A , B , & C , are used to construct a stock index. You have the following information regarding the three stocks for time = 0 ( now ) and time = 1 ( one year...