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The log-linear model is a form of Poisson regression that allows for the analysis of multi-way contingency tables.

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What is the appropriate analysis for this type of repeated measures multi-binary data?

There is a popular theory within psychology that certain emotions will trigger "prototypical" facial expressions defined by the simultaneous contraction of specific facial muscles. For example, if a ...
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Log-linear regression preferred over logistic regression for categorical vars?

I read here that, when all variables are categorical, log-linear is preferred over logistic regression "because log-linear is merely an extension of the chi-square test." I don't have a stats ...
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Conceptual question about log-linear analysis

I have measured the binary occurrence of three types of events on multiple days. Theory suggests that these events are not independent and should occur on the same days more than would be expected ...
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27 views

Difference between PROC CATMOD and PROC GENMOD for log-linear regression

I am reading "An Introduction to Categorical Data Analysis, Second Edition" by Alan Agresti. Data I am trying to fit is presented in Table 7.3 in the book. The log-linear regression by PROC GENMOD is ...
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50 views

How do I interpret the coefficients of a log-linear regression with quadratic terms?

I have a regression equation of this kind: $$\log {y} = a + bx + cx^2 + \epsilon$$ where $a$ is the intercept, $b$ and $c$ are the coefficients of $x$ and $x^2,$ and $\epsilon$ is the error. How do ...
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Log-linear analysis versus independent chi-squares result

I am analyzing a number of categorical variables, and used log-linear modeling in SPSS to see whether there is association between any of them. I have some variables, however, which turn out to be non-...
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41 views

How can I interpret intercept when my dependent variable is in log form?

My model consists of both log independent and dependent variables, and percentage share, as well as number of people and etc. My dependent variable is log(GPD per capita in USD), my statistic package ...
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1answer
38 views

Newton-Raphson Error

According to Agresti(2013) pg 364-365, iterative methods such as Newton-Raphson methods, $ \begin{aligned} \beta^\text{new} &= \beta^\text{old} + (X^{T}WX)^{-1}X^{T}(V) \end{aligned} $ help to ...
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Log-normal vs. log-linear vs. logging the response variable

I've been reading a lot of Wikipedia pages and StackExchange/CrossValidated posts, and I have come to a point where I realize I do not understand some of the terminology I have been using. What's ...
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44 views

calculate P-value loglinear coefficient marginal models fitted with maximum likelihood

i am using the cmm package in R to fit graph models between 4 categorical dummy variables of interest such that A is marginal independent from B B is conditional independent from A and B given D. I ...
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1answer
141 views

How are graphical models “a subset of log-linear models”?

Caveat lector: I am not sure what is meant by a "log-linear model". The Wikipedia page makes it seem as if log-linear model is an alternative term for exponential family. This description of a book ...
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1answer
54 views

Log-linear model vs Multinomial-Dirichlet model for contingency table

Given a 1x3 contingency table of the form $$[y_1,y_2,y_3]$$ where each $y_i$ represents a count on some random variable $$X\sim Multinomial(n, \pi_1,\pi_2,\pi_3)$$ We can estimate the vector of ...
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450 views

Poisson regression vs log-linear model

I'm confused about the difference between log-linear model and poisson regression and I am not sure which one to use to answer my research question. In the experiment, participants were grouped into ...
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1answer
73 views

What does it mean if the residuals for a log-linear model are all zero?

Probably a very basic question, but I have a contingency table formed of 3 categorical variables (one with 3 levels, the rest with 2) and have been asked to try to test the association between them ...
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68 views

How is a covariate added to a log-linear model?

There are a number of good Q/As about log-linear models (i.e., here). The data I am analyzing is off shifts between categories, 0, ...
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99 views

Bootstrapping in contingency table

I have categorical data represented by a two-way contingency table (say $Y_{1}$ and $Y_{2}$, each with three levels). The data consists of fully observed counts (where data on both $Y_{1}$ and $Y_{2}$...
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Present difference in estimates for positively-skewed continuous outcomes

I'm working with a dataset containing results from two types of cognitive tests: Pairs-matching test (say, $Y_1$), which recorded as number of incorrect matches (discrete count of mistakes, ranging ...
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488 views

semi-log (log linear) regression model

I know there are different reasons for choosing a particular model (e.g. log log, semi log, lin log). I read somewhere that the semi log (where only the log of Y is taken) corresponds to a ...
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Real-world implications of categorical interactions

I'm studying the interaction of three categorical variables but I'm struggling to explain what the interactions mean in real-world terms. The three variables each have two levels (yes/no). They are: ...
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1answer
44 views

Is there a multiple regression model with both percentage and unit changes in $Y$?

In a standard linear model, $Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2$, a unit increase in $X_1$ leads to a $\beta_1$ increase in $Y$ (likewise for $X_2$). In a log-level model, $\ln(Y) = \beta_0 + \...
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Distinguish 2-way and 3-way interactions in binary data, independent of reference category

$\newcommand{\P}{\mathbb{P}}$I have three variables $X_a, X_b, X_c \in \{0, 1\}$ and I define a joint distribution: $$ \P(X_a, X_b, X_c) \propto \exp \left \{ \theta_{abc} \mathbb{I}_{\{X_a = 0 \...
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1answer
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Effect Size log linear model when predictor is in percent

When performing a linear regression with a log-transformed dependent variable, one has to exponentiate the estimated coefficient of a predictor, subtract it by one and multiply it by 100 in order to ...
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53 views

Analysing count data for within-subjects design

I have the following experimental design but I'm not certain which analysis I should use to test my claim: I have a binomial outcome (correct, false = 1, 0). Each participant takes three questions, ...
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1answer
391 views

Log-linear regression vs. Poission regression

In this post, OP asked the difference between log linear regression and logistic regression. Two answers in the post are very clear and directly address OP's question. I understand Log-linear ...
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116 views

On the (wrong?) interpretation of log-linear models

For simplicity, let $X$ be a continuous random variable and assume that ${E}[\ln(Y)|X] = \beta X$, i.e., the conditional expectation of $Y$ given $X$ is proportional to $X$. According to many ...
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1answer
145 views

What distribution to fit if the log of log is still convex?

I am trying to fit a model with variable x, and y. plot(x, y) shows that it is convex (downward) and decaying which makes me think I need to make a log ...
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123 views

Log-linear analysis of transition matrices using R

I have some demographic transition matrices that I want to compare using a log linear analysis, but am having some trouble with model construction in R. I have read through several tutorials on log-...
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2answers
181 views

Check for endogeneity

I run a log linear model, as $log(y) = b_0 + b_1x_1 + b_2x_2 + e$. I think $x_1$ may be endogenous and I would like to test it, so that I can consequently run a two-stage model. I would like to know ...
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134 views

Analysing categorical variables across several categories (LogLinear analysis?)

I'm editing this question in hopes of improving it, and thus receiving some advice on it. I have collected info on diet from several populations. There are different groups (e.g. ElMolo) made of ...
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1answer
139 views

Nonlinear regression for a log-linear model

I have data points $(x_i, y_i), i = 1, \dots, N$, and a model (log-linear) with parameters $w_j, j = 0, \dots, m$ such that $y_i=\alpha_i e^{w_0+w_1x_i+w_2x_i^2+\dots+w_mx_i^m}+ n_i$, where $n_i$ are ...
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Bacteria counts in petri dish confusion

I'm currently (attempting) to help a fellow student with some statistical analysis. Basically she is looking at the effect of a sugar treatment on bacterial growth within a petri dish. She has three ...
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1answer
178 views

What's the difference in growth of Y in a linear regression model when using a log-lin model or a lin-log model

Description I'm currently studying a chapter on linear regression analysis. I have come to a section where we study the interpretation of the coefficients with logarithmically transformed variables. ...
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I want to find contributions of each independent variables

I would like to get contributions of independent variables (factors driving sales) in absolute dollar values. The log linear equation looks like this: $$\ln(\text{sales})=b_1 \times \ln(\text{...
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1answer
105 views

Multivariate Log-linear Model

I know from here that a log-linear model can be used to estimate a conditional probability of class $c$ given the feature representation $d$ of datapoint $x$. $p(c|d;\theta) = \frac{exp(\theta.d_c)}{\...
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2answers
157 views

Applied interpretation of coefficients of log linear regression model

I'm in the process of using a log-linear transformed OLS model to predict the impact of temperature changes on sales. I know that the interpretation of a log-linear model loosely follows as: for each ...
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1answer
930 views

What is the difference between Poisson Regression and Log-linear Models in terms of their usage and which should I use?

I'm currently analyzing a data set from an experiment, where participants could give one of three types of answers: 1) Correct, 2) incorrect-congruent, 3) incorrect-incongruent. The priming ...
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1answer
1k views

offset in glm for poisson regression

The offset argument in the glm() quite troubles me. As below, m3 is the usage of offset that I have seen. m4 is a manually calculated analog. But the result obtained is completely different, with m3 ...
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326 views

Log-linear model, Poisson regression, categorical variable with 100 levels

I want to compare the incidence rate(asum) of 100 different cities(cityID) to see if there are significant differences among them. Given that the incidence rate is following Poisson, so it is a log-...
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1answer
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problem with the relationship between log linear and logistic regression models

I am supposed to fit a logistic regression model and the find the log- linear model which correspond to it, fit that model and show the correspondence between parameters. But it is not working, I am ...
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79 views

Converting Dirichlet distribution to distribution on the log-linear parameters

Dirichlet prior/posterior provides a probability density on distributions over a multinomial variable. It has the form : $P(P) \varpropto \prod_i{P_i^{\alpha_i-1}}$ I can also describe the ...
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46 views

Standardising mean for variables and correct statistical approach

I'm working with data set which is highly skewed and not sure whether it is the the right approach to standardise the mean fro both dependent and independent variables. The aim is to find out if ...
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169 views

Is there an r package similar to LEM for analyzing contingency tables? [closed]

Is there an R package for log-linear analysis that is similar to LEM? Here is an example LEM script ...
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1answer
85 views

What's the name for the effect size of a log linear regression model?

I'm using a log linear regression to model a log transformed continuous positive variable, eg a quantity $Y$ that cannot be negative. eg: $$ log(Y) = \beta_0Const + \beta X$$ The coefficients of my ...
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1answer
111 views

Testing equality of proportions in several samples of the same individuals

I have data on sex and age of a population in different periods of the year, for several years. I want to test if age and sex ratios are the same across different moments of a year. I think a log ...
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1answer
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Interpretation of coefficient in log-linear model with share predictor

There are several questions on the interpretation of coefficients in log-linear models such as Interpreting regression coefficients of log(y+1) transformed responses Log linear model interpretation - %...
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343 views

What is the null model for a four-way contingency table?

I'm working through this tutorial on the Titanic data in R, a four-way contingency table, and I'm unclear as to what is the NULL ...
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1answer
478 views

Expected values vs. fitted values from log-linear model

Let's consider, for instance, a table like this one, with two independent categorical variables: x <- Titanic[,,2,1] I want to model this contingency table ...
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How to interpret a two-dimensional contingency table?

I am trying to understand how to interpret log-linear models for contingency tables, fitted by way of Poisson GLMs. Consider this example from CAR (Fox and Weisberg, 2011, p. 252). ...
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Cell count distribution assumption in loglinear modelling

In relation to loglinear analysis, SPSS gives two options for "Distribution of Cell Counts". The SPSS User Manual states: Assumptions. Two distributions are available in General Loglinear ...
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log-linear vs log-bilinear

I have seen these two terms used often. I can not really tell the difference between them they seem Identical to me. Can someone point me to a resource or give a simple explanation of what the ...