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

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Log linear analysis with weights

I am trying to conduct a log linear analysis using deer count data from Heisey (1985) and used as an example in Resource selection by animals by Manly (2002). They use a program named GLIM (...
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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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How to understand the constraint of loglinear modelling of zero-sum?

could anyone help explain to me how this constraint for loglinear models come about? Better with a concrete example of a contingency table? Thank you! c The context of the question: loglinear ...
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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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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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39 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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52 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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18 views

When is it sensible to use a nonhierarchical loglinear model?

Agresti (2002) writes on p317 that Nonhierarchical models are rarely sensible in practice. Using them is analogous to using ANOVA or regression models with interaction terms but without the ...
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30 views

Interpretation of coefficients

I know that probably a lot of people already asked about the interpretation of coefficients especially in log-linear models. Unfortunately, I was not able to find an answer to my specific question: I ...
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1answer
30 views

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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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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Dealing with sampling zeros

I would like to perform a $\chi^2$-test, but due to low sample size in some cases, I have sampling zeros. One example of such a case: ...
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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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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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Analysis of Categorical Data - Dichotomous Treatment with Multinomial Outcome

Imagine two groups in an educational experiment: treatment and control. Students in the treatment group receive targeted instruction on how to write a critical review, while students in the control ...
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1answer
41 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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MLE's of Log-linear parameters

Can the MLE's of the log-linear parameters (the constant, main effects and the interaction effects) be infinite even if cell counts and the margins in a contingency table are all positive ?
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57 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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Can I use log linear to analyse qualitative data?

I have large qualitative biological data I want to analyse (eg High/medium/low abundance; present/not present; burned/unburned). I also have a qualitative dependent variable. Can I use log linear to ...
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25 views

Loglinear modeling of a contingency table AxA' imposing marginal distributions other than observed

Anybody knows if it is possible to adjust loglinear models to a AxA' contingency table, using marginal distributions of A & A' other than observed? A & A' are the same variable measured in ...
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Sample Sizes Based on Cost Efficiency

I am planning a biology experiment that is testing the predictors of biological markers.These predictors are: Gender.(Binary) Smoking status.(Binary) Alcohol consumption.(Binary) Hiv infection ...
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462 views

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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259 views

How to interpret conditional odds ratios from a three-way contingency table?

I am trying to understand how to correctly interpret the estimated conditional odds ratios from a loglinear model on a three-way contingency table. This is an example from Agresti 2013 (p. 346, ...
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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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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 ...
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Ensuring parameters of log linear model sum to 1

I am training a log-linear model with parameters $\theta$ using SGD. I want to ensure that my parameters will end up being probabilities i.e. $\sum_i \theta_i = 1$. One way to do this is by using ...
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Log-Linear Dependent Variable Ratio beyond 1: how to interpret regressors

I do run a regression model with a dependent variable = ratio calculated G=y/x which provides values between 0 - 9 for extreme cases. I use a log-linear model for my calculus with various continuous ...
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Contributions of variables in Log-Log models [duplicate]

I have built a model on log(units) sold and want to measure the contribution of each independent variable in the model (which are also in ...
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77 views

Poisson regression: loglinear vs linear

In Poisson regression, there are two possible ways we can relate the dependent variable $y$ with the independent variables $x$: $E[y|x] = w^Tx$ $E[y|x] = e^{w^Tx}$ The likelihood functions are: $...
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1answer
102 views

loglinear analysis, assumptions met?

We've data from a large ongoing project at a big science museum. We are showing people plates of food where we vary the plate shape (round or square; 0,1), food arrangement (polygonal or vertical ...
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56 views

Sample size log linear analysis?

Is there a rule of thumb for the sample size for a log linear analysis? For example, would it be inappropriate to use this analysis for a sample size of 50 with 3 predictors?
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$\chi^2 $ of multidimensional data

I want to test if two observations of nominal data accord to the same distribution. I am using the chi squared statistics to perform a chi squared homogeneity test and normalize the result with Cramer'...
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What's the right interpretation for parameter estimates in loglinear modelling?

I'm doing a loglinear analysis of the following data. Male is coded as 1, Female as 2. Senior workers are coded as 1, middle level as 2, and shopfloor as 3. A is coded as 1 and is the most ...
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Interpreting dummy variable in semi-log model

There are numerous theories on how to interpret the coefficients of dummy variables in a semi-log model but I still am not sure about it. Do we multiply the coefficient by 100 to get the change like ...
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Advice for test on categorical variables

I am working with two variables - variable 'A' is an independent categorical variable and has three levels 'a' 'b' and 'c'; variable 'B' is continuous response variable data I have classified into ...
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1answer
119 views

Using contingency tables for testing multiple dependencies

I know that I can determine the correlation / association / dependency between two variables (X= smoker, and Y=cancer) using chi-squared with a 2x2 contingency table: ...
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How do I find the odds ratio using the output of a loglinear model?

This was a homework problem from Agresti (7.2) that I didn't get, even after looking at my class' solutions. Help? So we are given the output of a loglinear regression ($λ_{ij}^{XY}$). The output is: ...
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Regression Model for Binary Matched or Paired Contingency Table Results

This is a follow-up question on a prior thread about the same setup as follows: We have two "Methods" ("A" and "B") to diagnose a medical condition. We are not trying to determine which one is better ...
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Correlated Proportions shown in a Mosaic Plot. What is the fitted model that generates residuals?

I have a 2-by-2 table of correlated proportions where I am plotting the positivity of two diagnostic methods applied on a sample of 216 individuals: ...
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Comparing Proportion of Positive Tests

A condition or disease (D) is measured using two different methods (A and B) in a sample of 1,000 individuals from a population. Using method A, the percentage of positive cases is 25%, whereas method ...
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155 views

Antilog of a semilog regression model with dummy variables

I have a semi-log regression model, with two continuous predictors, two categorical predictors (0 or 1 dummy variables) and a non-zero intercept. The response variable is log10 transformed, none of ...
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1answer
212 views

Selecting the best subset of features in binary logistic regression [duplicate]

I am using a binary logistic regression (a type of probabilistic statistical classification model, is used to predict a likelihood of belonging to a class (True, False)). I have 4 features and I want ...
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492 views

Fitting a heteroscedastic generalized linear model for binomial responses

I have data from the following experimental design: my observations are counts of the numbers of successes (K) out of corresponding number of trials (...
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Linear regression with log dependent variable

I have the following regression: $log(Y) = \alpha + \beta X + \epsilon$ with $E[\epsilon] = 0$ and $var(\epsilon) = \sigma^2$. There is no assumption on the distribution of the errors $\epsilon$. In ...
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Type of inference to use with log-linear Poisson glm on contingency table frequency counts

I was doing some log-linear models to test for interactions/associations in multiway contingency tables (based on the tutorial here, http://ww2.coastal.edu/kingw/statistics/R-tutorials/loglin.html). I ...
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Log Linear Models: Interpretation when None Fit

This is question 9.6 from Categorical Data Analysis by Alan Agresti (Wiley, 2013). The question asks us to find a Log Linear with the best fit for a 2x2x2 contingency table. The following are the ...
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Exploring dependencies between variables in log-linear models

Hi there I'm using R to perform some multivariate data analysis on health data. I'm currently using the glm() function with <...