Generalized Linear Models Overview

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Questions and Answers

Which of the following is NOT a valid reason for using variable transformations in a statistical model?

To capture non-linear relationships between variables.
To improve the fit of the model to the data.
To account for interaction effects between variables.
To ensure that the data meets the assumptions of the statistical test. (correct)
To allow for a more accurate prediction of the mean response.

Which distribution is most suitable for modeling the number of defective items in a sample of 100?

Poisson
Bernoulli
Exponential
Binomial (correct)

In the context of Generalized Linear Models (GLMs), what is the purpose of the link function?

To control the variance of the response variable.
To transform the response variable to a more suitable distribution.
To connect the linear predictor to the mean of the response variable. (correct)
To account for the presence of nuisance parameters.
To ensure the linearity of the relationship between the predictor variables and the response variable.

What is the general form of a distribution from the exponential family?

$f(y; \theta) = exp[ \frac{y \theta - b(\theta)}{a(\phi)} + c(y, \phi)$ (D) Signup and view all the answers

Which of the following is NOT a component of a Generalized Linear Model (GLM)?

Nuisance parameter (E) Signup and view all the answers

Which of the following is the primary difference between a Generalized Linear Model (GLM) and a Generalized Linear Mixed Model (GLMM)?

GLMMs allow for the inclusion of random effects, while GLMs do not. (C) Signup and view all the answers

Which of the following is NOT considered an advantage of using Generalized Additive Models (GAMs)?

GAMs are simpler to interpret than GLMs. (H) Signup and view all the answers

In which scenario would a Generalized Additive Model (GAM) be particularly advantageous over a Generalized Linear Model (GLM)?

When the relationship between the predictor variables and the response variable is non-linear and complex. (D) Signup and view all the answers

What can we say about the residuals in a linear regression model if the independence assumption is NOT met?

The residuals are correlated with each other. (D) Signup and view all the answers

What is the major difference between a Generalized Linear Model (GLM) and a Generalized Additive Model (GAM)?

GAMs allow for non-linear relationships between the independent variables and the dependent variable, while GLMs restrict these relationships to be linear. (A) Signup and view all the answers

Which of the following is a major advantage of using a Generalized Additive Model (GAM) over a Generalized Linear Model (GLM)?

GAMs allow for a more complex and realistic representation of the relationship between the independent variables and the dependent variable. (C) Signup and view all the answers

Which of the following statements BEST describes the key distinction between a Generalized Additive Model (GAM) and a Generalized Additive Model for Location, Scale, and Shape (GAMLSS)?

GAMLSS models the mean, variance and shape of the response variable, while GAMs model the mean only. (B) Signup and view all the answers

In a simple linear model (LM), which of the following is NOT an assumption about the errors (ε)?

Errors are linearly dependent on the independent variable. (B) Signup and view all the answers

What is the typical interpretation of a p-value in analyzing data using a Generalized Linear Model (GLM)?

It represents the probability of obtaining the observed data, assuming the null hypothesis is true. (C) Signup and view all the answers

What is the main limitation of a Generalized Linear Model (GLM) that is addressed by a Generalized Additive Model (GAM)?

GLMs assume a linear relationship between the dependent variable and all independent variables, a restriction that GAMs overcome. (B) Signup and view all the answers

Which of the following is NOT a characteristic of a Generalized Additive Model for Location, Scale, and Shape (GAMLSS)?

GAMLSS models assume a linear relationship between the independent variables and the response variable. (A) Signup and view all the answers

Which of the following is NOT a characteristic of GLMs compared to LMs?

GLMs assume that the response variable is normally distributed. (A) Signup and view all the answers

What is the main difference in the response variable distribution between LMs and GLMs?

LMs assume a normal distribution, while GLMs allow for distributions from the exponential family. (B) Signup and view all the answers

Which of the following is NOT true about the link function in LMs and GLMs?

The link function in LMs is always linear, while the link function in GLMs can be non-linear. (A) Signup and view all the answers

What is the main reason why LMs are often not suitable for non-normal data?

LMs assume that the response variable is normally distributed, which may not be the case for non-normal data. (A) Signup and view all the answers

What is the key concept that distinguishes GLMMs from GLMs?

GLMMs allow for random effects, while GLMs do not. (D) Signup and view all the answers

What is the defining characteristic of GAMs?

GAMs use non-linear functions to model the relationship between the predictors and the response variable. (C) Signup and view all the answers

What is the key advantage of GAMLSS (Generalized Additive Models for Location, Scale, and Shape) over other models like GAMs and GLMMs?

GAMLSS allows for the modeling of the mean, variance, and distribution of the response variable. (D) Signup and view all the answers

Which of the following is NOT a common application of GAMs?

Predicting stock prices in finance. (B) Signup and view all the answers

Flashcards

P-value

A measure indicating the strength of evidence against the null hypothesis. A value larger than 0.05 suggests weak evidence.

Polynomial effects

A method to model non-linear relationships by adding polynomial terms to account for diminishing returns, e.g., study hours and exam scores.

Interaction effects

Modeling that captures how the relationship between one variable changes at different levels of another variable, e.g., study hours and past scores.

Nuisance parameter

A parameter influencing the model but not of primary interest, often treated as constant to enhance model accuracy.