A generalization of linear regression allowing for nonlinear relationships via a "link function" and for the variance of the response to depend on the predicted value. (Not to be confused with "general linear model" which extends the ordinary linear model to general covariance structure and ...

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Predict after using Box Cox Transformation

I am doing a Multiple Linear Regression on a data set where: The response variable is continuous One of the explanatory variables is continuous and the rest are binary(categorical) 1 if it is there 0 ...
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17 views

Make sense of contrast in general linear model (GLM)?

I understand how to make sense of the design matrix in a general linear model (GLM). Basically, each column of the design matrix describes one condition under which the data are observed. For ...
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4 views

Mixture of binary or multinary columns in design matrix?

I am designing the design matrix for my general linear model (GLM). Besides the dummy constant column, I wish to have 4 regressors (columns) in my design matrix. They are diagnosis, age, gender, and ...
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202 views

Can I model standard deviations in a linear model?

Is it possible to put standard deviations or variances into a linear model, as the data to be explained? I have a predictor which I think will linearly increase the standard deviation of a measure, ...
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17 views

Linear model with longitudinal data, predicting difference

I have a set of data for 2 visits in patients and I would like to see whether there is a effect of a difference of one variable on another. So, lets say, my variables are A, B, age + gender. I want ...
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30 views

Is it possible to get a covariance matrix of fitted values for a GLM model in R?

I would like to get a covariance matrix of fitted probabilities for a logistic regression model in R. I would like to do this because I want to find the variance of the difference between the two ...
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58 views
+100

Can correlated random effects “steal” the variability (and the significance) from the regression coefficient?

I have time-series count data $N_{i,j}$ (population sizes in site $i$ and year $j$) and I want to correlate year-to-year changes with the environmental conditions $x_{i,j}$. For this, I am fitting ...
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22 views

How to apply transformations to the predictors of a GLM?

This post discusses why we need to transform $Y$ before estimating the predictors exponents in order to reduce the problem to a linear fit. The example builds on $Y$ log-normal. In the case of a GLM, ...
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50 views

How to calculate confidence intervals in a GLM using the profile likelihood?

I've been trying to better understand how JMP does regression and associated models. I can compute the correct parameter estimates for a GLM, by using iteratively re weighted least squares. But now ...
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35 views

Can someone look at my method for fitting a GEE to my data?

I’ve been doing some statistical analyses in R on some data. It’s for use in a manuscript I’m hoping to get published in a biological journal. Unfortunately, the tests I ended up having to run are ...
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1answer
17 views

GLM link function for bimodal probit fitting?

I am trying to model a set of data I have physical reason to believe can be represented by a bimodal normal cumulative distribution function (Technically it is a bimodal log-normal CDF, but I think I ...
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49 views

Why do my boostrapped CI's (using boot.ci in R) not include the point estimate?

I'm interested in estimating an average treatment effect $$ \operatorname{ATE}\left(A', A''\right) = \mathbb{E}\left( Y\ |\ A'' \right) - \mathbb{E}\left( Y\ |\ A' \right) $$ with a generalized ...
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20 views

Best way to examine mortality tables?

I have a set of tables containing mortality rates (hazard rates) and I want to see how well these values reflect the influence of the covariates (age, sex, issue year, etc.). I also have actual ...
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44 views

Random variables of mixed models

I am thinking about using mixed models as part of my research, but I am having trouble understanding its application. In particular, I have two somewhat related questions regarding mixed models. ...
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10 views

Fisher information and asymptotic covariance matrix [duplicate]

I am reading the Categorical Data analysis by Dr. AGRESTI. Here, it explains "The liklihood function of for the GLM also detemines the asymptotic covariance matrix of the ML estimator Beta_hat. This ...
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32 views

When to use zero-inflated poisson regression and negative binomial distribution

I have a fairly simple dataset looking at the relationship between the first nesting date of a bird in a given year (Date) and the birds overall fledgling production from that year (Fledge; count data ...
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80 views

Model selection using an artificially insignificant covariate

This is continued from my other post on model selection. Let me provide more details first. 1) I have a factorial design. Factor A has 5 levels, B has 2 levels, C has 2 levels. Let us assume that ...
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16 views

how to interpret Interaction term in generalized linear model [duplicate]

I have an experimental condition (dummy-coded) as an categorical predictor, and one continuous predictor variable (treatment frequency). The dependent variable (Y) is consumer satisfaction This is ...
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14 views

Partial pseudo $R^2$ with GLMs

Is a partial pseudo $R^2$ (pseudo $\eta^2$?) even a valid concept when dealing with a GLM? This, of course, presumes that partial pseudo $R^2$ is valid at all. If it is valid, how would one go about ...
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34 views

R: Prediction using glm() [migrated]

I am using glm() function in R with link= log to fit my model. I read on various websites that fitted() returns the value which we can compare with the original data as compared to the predict(). I ...
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13 views

Pareto two-tailed GLM regression

How can I perform a Pareto two-tailed GLM regression? Any reference to link functions and code in R?
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1answer
16 views

GLM Prediction Variance with Average Observations

Suppose I have data set where the observed values are averages and not necessarily individual data points. For example, suppose record 1 has the observed value of $Y_1 = 2.0$. However, I know that the ...
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1answer
22 views

Modeling remaining duration for prediction

Suppose we're in the business of repairing broken specialty widgets and reselling them. At each point in time, we want to predict how much cash we'll make in the next 30 days on the existing ...
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36 views

adjustment of covariates in linear model

I am trying to understand the adjustment of covariates in the linear model such as multiple logistic regression. How does adding a covariate adjusts the coefficients for that covariate (any intuitive ...
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63 views

linear regression intercept does not match

I have done a linear regression in R, using glm function. The calculated intercept says 0.98, but when I plot it, it does not seem to hit the estimated intercept on Y axis. Its far below. Here are my ...
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30 views

A non-negative definate matrix has a non-negative generalized inverse

I'm having trouble proving a N.N.D matrix has a N.N.D G-Inverse. So far I have: If we assume x = Az where x >= 0 and A is a nnd matrix. So if Y is a G-inverse than: x = Az = YAz = Yx >= 0 . Thus ...
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51 views

What is the difference between GLM and splines?

Suppose we want to predict $Y$ given the following $X$ observations: ...
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1answer
14 views

conditional independence in repeated measures design

How the responses are independent when conditioned on random effect in repeated measure analysis (linear mixed model)?
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45 views

Interpretation of $\theta$ in negative binomial regression

First off, a very similar question has been asked before. But the answers to this question did not explain what high/low values of theta mean. Here's my crack at trying to figure out what high/low ...
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1answer
24 views

model comparison when alternatives are not all nested within one another

I am running a glmm with three fixed effects: opponent 1 size ("1") opponent 2 size ("2") opponent 1 size - opponent 2 size ("diff") I am unable to run all three variables in the model at once ...
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68 views

What properties of a likelihood function are required for quasi-likelihood estimation?

Quasi-likelihood seems like a great way to use Iteratively Weighted Least Squares to fit linear linear models with a very general class of likelihoods. But what is that class? Obviously the ...
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15 views

Struggling with non-normality in generalized linear model

Dear statistics experts, I am looking for correlations between certain measures of brain structural integrity (fractional anisotropy, given as ratio between two hemisphere ==> rational data range ...
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120 views

Increased Type I error - GLM

Some of you might have read this nice paper: O’Hara RB, Kotze DJ (2010) Do not log-transform count data. Methods in Ecology and Evolution 1:118–122. klick. In my field of research (ecotoxicology) ...
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12 views

GLM post hoc with non-parametric tests?

I have a question regarding the appropriate use of comparisons for independent samples (3 factor levels). Overall sample size is N=546, subsamples: 218 or 228 or 100), convenience sampling, ...
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42 views

How do I choose between a simple and a mixed effect logistic regression?

I have a list of predictor variables to put in to a logistic regression model. How I know that should I do a simple logistic regression (using glm function in R) or ...
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20 views

How to model when actionable data is generated on a daily basis

Trying to build a predictive model for attrition prediction of service desk agents using logistic regression. Data available: Daily performance metrics such as call quality,avg. call ...
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16 views

How to do planned comparisons on repeated measures (GLM repeated measures) using SPSS?

I have issues figuring out how to perform planned comparisons using a GLM for repeated measures analysis. More specifically, I have one group of subjects, assessed with 2 different scales (3 subscores ...
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173 views

How to choose data for training a predictive model for attrition prediction

Trying to build a predictive model for attrition prediction at service desk/call center. Have daily data on the following parameters: 1.Call quality - QTM (0-100%), 2.No. of calls - Calls(Number) ...
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1answer
36 views

Multiplicative error and additive error for generalized linear model

If the following generalized linear model was used, how should I interpret the error term? link function: natural log distribution: Gamma distribution i.e., $\ln E(Y)=X\beta$ and $E(Y)=\exp(X\beta)$ ...
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1answer
64 views

How to model a count dependent variable with upper limitation

I have a dependent variable, which have 0, 1, 2, or 3 for its value. I asked participants to choose three items and coded 1 if it is in a certain category and 0 otherwise. I add the three binary ...
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21 views

Zero inflated model problem: system is computationally singular

I'm using R.After getting an error asking me to provide starting values for a glm (poisson family), I took a look at my data and realized I had quite a bit of zeroes. So, I tried zeroinfl from pscl. I ...
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31 views

Confidence interval for a regression parameter via prediction

Consider a simple Poisson-regression - GLM - model. There $\exp\left(\beta\right)$s are used as Incidence Rate Ratios (IRR), but their calculation is sometimes not completely straightforward, for ...
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15 views

GLMM - time or day/date as a random factor

I have searched for many days trying to find the answer to this question, and am still not 100% sure I am happy with my conclusion. I am interested in looking at the effects of environmental variables ...
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54 views

Identifiability in generalized linear random effect model?

Suppose I observe binary $Y_{ij}$ for $i = 1, ..., N$ and $j = 1, ..., J$ and I want to model $$\Pr(Y_{ij} = 1 \mid \lambda_{i}) = \Phi(\lambda_{ij}), \qquad [Y_{ij} \perp Y_{ij'} \mid \lambda_i]$$ ...
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1answer
39 views

Regressing, analysing data with points rather than polynomial?

I am looking into making a regression of a bunch of data that is contained on some range of real numbers. In my case, x is between 0 and 1 and y is between 0 and 10. If I have 150 data points on this ...
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1answer
30 views

Is it acceptable to not include high-order interactions (3-way and above) in the model when they are not by themselves of interest?

Is it acceptable to not include high-order interactions (3-way and above) in the model when they are not of interest and not part of the hypothesis that is being tested? NB. I am not talking about ...
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43 views

Help with complex model formula in lmer (lme4) for R

Most examples about lmer formula description in R target rather simple study designs. However, sometimes one is confronted with more complex designs and there is no ...
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2answers
89 views

Sine link with binary regression

I have used the SIN link to estimate probabilities, mostly with Program MARK. However, I am not sure how the SIN link works. I know the SIN link enables parameter ...
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24 views

How to deal with categorical features.

Recently I am playing in the famous Big-Data website Kaggle. There is a Display Advertising Challenge. In this competition, you are giving a training file which include huge records. the records is ...
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48 views

Numerical stability of IWLS for Gamma models with log-link

The combination of a $\Gamma$-distribution with the log-link function in a generalized linear model can be a useful model. However, in my experience the iterative weighted least squares (IWLS) ...