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Questions tagged [log-linear]

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

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Appropriate way to visualize significance in 2x3 contingency table using mosaic plot

I've checked multiple threads about handling or visualizing contingency tables, but can't find one that can help my current question. I have a 2x3 contingency table: "group" variable has 3 levels not ...
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Interpreting log-linear model for contingency table in R

I'm looking at sample data and trying to determine whether there is any association between the height of the husband and that of the wife below. I don't fully understand what the symbolic ...
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Difference between null and saturated log-linear models

I have data from an experiment testing the number of 'cases' at each of three measurement points (0, 12, and 24 weeks). I am interested in whether the proportion of cases across these measurement ...
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28 views

Interpretation of a log-level regression in its associated 'level' form

Is it conventional to interpret a least-squares regression with a log-transformed dependent variable (log-linear model) in its "level" form? In other words, running a model with the outcome in 'log ...
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Parameters, constraints and MLE of log-linear models

I want to use log-linear models to assess the type of (in)dependence between variables in $2\times2$ and $2\times2\times2$ contingency tables. In the process of doing so I would also like to ...
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48 views

Log-linear difference-in-differences

I am estimating several linear models using a difference-in-differences (DiD) framework. The model interacts a treatment indicator (i.e., 1 for the treatment group, 0 for the control group) and a "...
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16 views

When to use a multicategory logit model versus a loglinear model?

Do you only use the baseline-category logit model when categorical responses have more than 2 categories? How is this different than the loglinear model, which is useful when at least 2 variables in ...
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Log-Linear Output Help

I ran a loglinear model with 3 variables. Internet Use (Y/N), Nervous Breakdown(Y/N), and Happiness (3 levels). I understand by two way interactions are significant, but I am getting lost trying to ...
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logliner analysis on SPSS with more than 10 variables

I want to run logliner analysis on SPSS Statistics 25 but I have more than 10 variables.= 1 outcome variable and 11 predictors/factors. The big number of factor variables can be explained by the fact ...
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Log-linear regression: interpretation of RSE

AIM: To really, really understand what the model outputs mean in a log-linear regression, specifically, how to interpret the residual standard error (RSE). I have read this post but it does not ...
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242 views

Confidence interval of a log-linear regression

AIM: Make a confidence interval statement on a log-linear regression I have read posts like: Interpreting Standard Deviation of Natural Log Transformed Data Lognormal Regression? But they do not ...
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INTERPRET A REGRESSION MODEL WHEN OUTCOME VARIABLE IS LOG TRANSFORMED [duplicate]

I have used a linear model between a log-transformed outcome variable and a group of predictor variables. In this model, the dependent variable is in its log-transformed state, and the independent ...
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Log-linear BIAS adjustment

I have a loglinear model of: $log(\mu(S_{ij|gij}))=\alpha_0+\alpha_1g_{ij}$ where gij is distance, and Sij is connectivity There is a bias in the distribution of count values for the outcome ...
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58 views

Poisson log linear Regression: using either R or python

I was hoping someone can help me with this problem. I posted a similar question earlier but it's not the same. I have the following: A 2x2 matrix of structural connectivity values between brain ...
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2answers
114 views

Interpretation of β in case of log-lin model for relationship between X and Y

In many papers, the dependent variable is transformed by taking natural log. For instance, consider the following model: $$\newcommand{\Cov}{{\rm Cov}} \ln(\text{Y}) = \alpha + \beta\, X_1 + \epsilon ...
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Logistic regression and log-inear

I do not know why log-linear is non-sensitive margins and logistic regression is sensitive margins. Both are using odds ratios Can anyone give some explanation.
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483 views

Predicting probabilities after log-linear regression

I would like to estimate a log-linear regression and examine the results with Stata's marginsplot command. I have transformed my dependent variable into natural logarithm (to make a highly skewed ...
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347 views

Check log-linearity of a continuous variable to predict survival

I have the following survival data: cases with a continuous variable risk_factor wich higher values having a higher HR (1.026, CI: [1.017-1.034], p = 2.03e-09) for ...
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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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117 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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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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81 views

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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450 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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47 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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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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79 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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899 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
133 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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102 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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148 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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842 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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45 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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123 views

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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753 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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135 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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161 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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168 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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300 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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179 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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254 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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301 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
116 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)}{\...