Tagged Questions

Refers to any model where the a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

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Regression with correlated explanatory variables

I have variables of the following kind (coded in R): ...
94 views

Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
187 views

Python packages for numerical data imputation [closed]

I am working with multivariate numerical data with a lot of missing values (so dropping all entries or columns with missing data is not an option). Is there a Python package for data imputation? I ...
51 views

How to analyze repeated measurements in two matched but unequal samples

For a manuscript intended for submission to a medical (or psychological) journal, I have cognitive data from 16 patients and 32 age- and gender-matched healthy controls at four time points ...
67 views

Partitioning the appropriate error term in a repeated measures R

Basically I have a repeated measures experiment with two reward levels and two speed levels. Every trial participant can be randomly presented with highReward*slowSpeed or lowReward*fastSpeed etc., ...
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What are typically encountered condition numbers in social science?

As part of my thesis, I'm proving (or attempting to prove...) a few asymptotic results. Because these results depend on the condition number, I'd like to have some idea about the typical sizes of a ...
70 views

When to take logarithms of a variable such as the Herfindahl Index?

Currently I am skimming through a couple of papers in well established journals! I became curious when I found papers with linear regression models using the Herfindahl index as the dependent ...
145 views

How to test whether linear models fit separately to two groups are better than a single model applied to both groups?

My question is how to tell if two regressions explain the data better than one. Let me be more concrete with an example (which I'm making up as I go, it's not meant to be plausible). Say I'm ...
124 views

Difference between effect size (partial $R^2$) and coefficients

I am working with spoken language data and use linear models do determine the relationship between different phonological processes in my data. Background Measures of the regularity of syllable ...
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How does I bias my standard errors estimates when I forget to correct for autocorrelation of errors?

Suppose that I have a linear model with autocorrelated errors. Is there any results telling me that if I assume iid errors I overestimate or underestimate my standard errors ?
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What extra properties does assuming errors are iid have compared to assuming errors are uncorrelated and common variance

In linear regression model, the means of the errors are assumed to be zero. Furthermore, we can assume either that the errors are uncorrelated and have the same variance, or even that the errors are ...
87 views

Assumptions in general linear model and in multivariate linear regression model?

I am reading Wikipedia and some notes I found online, and still not very clear about their definitions. Both the general linear model and the multivariate linear regression model assume  Y = X\beta ...
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Conceptual explanation of regression coefficient?

I understand, mathematically, how to get the estimates of coefficients in ordinary least squares. What I am struggling with is coming up with a conceptual, geometric explanation for the correlation ...
124 views

How can a multiclass perceptron work?

I don't have any background in math, but I understand how the simple Perceptron works and I think I grasp the concept of a hyperplane (I imagine it geometrically as a plane in 3D space which seperates ...
80 views

Using percentiles as predictors - good idea?

I am thinking about a problem which is to predict log(spend) of a customer using linear regression. I am considering what features to use as input and wondering if it would be OK to use the ...
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Likelihood ratio test to compare two predictions

I have two predictions from two different types of methods. "predictedHousePrices1" is a continuous variable and the output of a prediction from a RandomForest model, "predictedHousePrices2" is the ...
86 views

Guessing the correlation structure of a mixed model

If you would fit a small sample like with the standard framework for linear models. Would you suggest from the residuals any special correlation structure like compound symmetry or first order ...
86 views

Using the covariance matrix to calculate correlations

I'm a bit lost here. I have a matrix of response variables, $y$, and I fit a model to account for a number of predictor variables, say $x_1$, $x_2$ and $x_3$: ...
118 views

Log likelihood improves with addition of a nonsignificant variable

In this question I asked about changes to AIC when adding a variable. It turns out to be partly due to the way SAS figures AIC. However, I now have two models where the log likelihood improves a lot: ...
76 views

Clustering using correlation of residuals

I have worked out a naive approach for clustering different variables, and I wonder what better approaches are there. I have data with many more dimensions (variables) than observations (samples), and ...
275 views

(Why) do overfitted models tend to have large coefficients?

I imagine that the larger a coefficient on a variable is, the more ability the model has to "swing" in that dimension, providing an increased opportunity to fit noise. Although I think I've got a ...
79 views

Linear regression simulation

I would really appreciate if someone could help me with this question. I want to simulate $n$ datasets in R with eight predictors where $Î²=(3,1.5, 0, 0, 2, 0, 0, 0)$ and the pairwise correlation ...
49 views

Running linear mixed effects model with Amelia package - How to run model diagnostics?

I'm trying to run a fairly simple linear mixed effects model in R, using the Zelig model ls.mixed (multi-level least-squares ...
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Excluding one combination of two factors in a linear model

Imagine you are modelling an outcome based on two discrete factors, factor1 and factor2, which can be yes or no. You could do ...
155 views

Inclusion of significant interaction term in logistic regression table versus stratification for data presentation

This is a general question on logistic regression result reporting for a publication. We have an example where two well correlated ($r=0.4, p=0.001$) blood parameters (...
120 views

F test and t test in linear regression model

F test and t test are performed in regression models. In linear model output in R, we get fitted values and expected values of response variable. Suppose I have height as explanatory variable and ...
93 views

Fraction of variance unexplained and R-squared in linear and non-linear regression

I have a non-linear model of the following form: $y = a*x^b$ I can fit it using logarithms and a linear model or directly with a non-linear model. First approach, logarithms and linear model: ...