Prove that if [operatorname{logit}left(operatorname{Pr}left(y_{i}=1 mid mathbf{x}_{i} ight) ight)=beta_{0}+mathbf{x}^{top} boldsymbol{beta}] and [operatorname{logit}left(operatorname{Pr}left(y_{i}=0 mid mathbf{x}_{i} ight) ight)=alpha_{0}+mathbf{x}^{top} boldsymbol{alpha}] then

Question:

Prove that if

\[\operatorname{logit}\left(\operatorname{Pr}\left(y_{i}=1 \mid \mathbf{x}_{i}\right)\right)=\beta_{0}+\mathbf{x}^{\top} \boldsymbol{\beta}\]

and

\[\operatorname{logit}\left(\operatorname{Pr}\left(y_{i}=0 \mid \mathbf{x}_{i}\right)\right)=\alpha_{0}+\mathbf{x}^{\top} \boldsymbol{\alpha}\]

then $\beta_{0}=-\alpha_{0}$ and $\boldsymbol{\beta}=-\boldsymbol{\alpha}$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Categorical And Count Data Analysis

ISBN: 9780367568276

2nd Edition

Authors: Wan Tang, Hua He, Xin M. Tu

See More Books

Question Posted: Mar 30, 2024 07:00 AM

See More Questions

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
The population logit model of the binary dependent variable Y with multiple regressors is Pr left parenthesis Upper Y equals 1 vertical line Upper X 1 comma Upper X 2 comma ... comma Upper X...
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
The accompanying table shows proportions of computer salespeople classified according to marital status and whether they left their jobs or stayed over a period of 1 year. a. What is the probability...
Raddington Inc. makes and sells chairs. The controller is responsible for preparing the master budget and has accumulated the following information for 2012: Raddington Inc. has a labour contract...
The Towson Manufacturing Corporation applies overhead on the basis of machine hours. The following divisional information is presented for your review: Find the unknowns for each of thedivisions....
A current is detected in a photoelectric-effect experiment when the cathode is illuminated with green light. Will a current necessarily be detected if the cathode is illuminated with blue light? With...
Valley Products, Inc. is considering two independent investments having the following cash flow streams: Valley uses a combination of the net present value approach and the payback approach to...
Stephen purchases a home on December 7, 2012, for $430,000. He lives in the house for a year but moves out in December, 2013. In 2014, he takes a $10,000 deduction for depreciation on the property....
If $\Sigma$ is an $n \times n$ invertible matrix and $K$ is a $k \times n$ matrix with $\operatorname{rank} k(k \leq n)$, show that $K \Sigma K^{\top}$ is invertible.
Consider a random variable $x$ following the standard logistic distribution with the $\mathrm{CDF}$ and PDF given in (4.3) and (4.4). (a) Show that the PDF in (4.4) is symmetric about 0. (b) Show...
Find the exact function value, if it exists. tan ( -600)
Ask if your family has a diamond. Can you piece together its biogra- phy, its social life? Was it a purchase or a gift? What stories are asso- ciated with it, and what does it mean to its owner? Do...
How do micro-level theories, including rational choice theory, social exchange theory, and dramaturgical theory, elucidate individual decision-making, social interactions, and the construction of...
How do classical and contemporary social theorists conceptualize the intricate interplay between agency and structure in shaping human behavior and societal dynamics ?
We will delve into the profound significance of sustainability issues that are impacting the world of business and development. As we embark on our journey through the realm of green finance, it's...
Define the term Biological Psychology. Explain why it may be important to study biology in a psychology course? Include how can biology affect behavior. Include how can biology affect cognition
In Figure P28.21, show how to add just enough ammeters to measure every different current. Show how to add just enough voltmeters to measure the potential difference across each resistor and across...
Write a while loop that uses an explicit iterator to accomplish the same thing as Exercise 7.3. Exercise 7.3. Write a for-each loop that calls the addInterest method on each BankAccount object in a...
a. What is the difference between moving average and weighted moving average? Using four periods data for January, February, March and April as 100, 104, 95, 99 find the moving average and a weighted...
B. A firm has classified its customers in two ways: (1) according to whether or not the account is overdue, and (2) whether the account is new (less than 12 months) or old. An audit of company...
5. Write a shell script that contains a hashpling and comments. It should perform the following tasks: a. Displays a list of currently logged-in users b. Displays the system's host name c. Displays...

Prove that if [operatorname{logit}left(operatorname{Pr}left(y_{i}=1 mid mathbf{x}_{i} ight) ight)=beta_{0}+mathbf{x}^{top} boldsymbol{beta}] and [operatorname{logit}left(operatorname{Pr}left(y_{i}=0 mid mathbf{x}_{i} ight) ight)=alpha_{0}+mathbf{x}^{top} boldsymbol{alpha}] then

Question:

Step by Step Answer:

To prove that beta0 alpha0 and boldsymbolbeta boldsymbolalpha we start by defining the logistic func...View the full answer

Applied Categorical And Count Data Analysis

Students also viewed these Statistics questions