Questions tagged [regression]
Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.
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Standardizing OR from logistic regressions with log-transformed variables for meta-analysis?
I´m trying to meta-analyze odds ratios from logistic regressions; some of which log-transformed the independent variable first.
(i.e. some studies present an OR per +1 in the independent variable, ...
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Why isn't X treated as a random variable in linear regression MLE? [duplicate]
I am very confused by this because when I watch videos or read about MLE with linear regression it seems to be commonly assumed that $X$ is fixed or that if it is random we don't care for the purposes ...
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Relationship between the t-statistic of a coefficient in an OLS multivariate regression and Ridge shrinkage?
If I'm running a multivariate OLS regression and look at the t-stats of coefficients, is it the case that the coefficients with smaller t-stats are shrunk relatively more if I were to run the same ...
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Is it possible to have better results by PCA PCs in compare to Laplacian eigenmap
Suppouse I have a data set of the form $p = 200$ and $N = 35$. I am interesting in the multiple linear regression model train, for this reason I need somehow simplify my data. I decided to use two ...
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Semi-parameteric estimation
I am interested in the effect of certain interventions $T$ on my value of interest $Y$, my model is,
$$Y = \tau f(T, X, Z) + g(X, Z), $$
where $f(T, X, Z) = T \times X + T \times Z$ , that is all the ...
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pls with constant variable
I am using Partial Least Squares (PLS) to predict the outcome variable Y. Prior to running the PLS, I included a column of 1 in the independent variable dataset X as a constant variable. However, I ...
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Cox Regression: handling a time interval of drug administration when only given once
I would like to investigate the effect of a drug on survival with Cox regression. The drug can be administered either once or twice. In the univariate Cox regression, I see that a shorter time ...
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How to deal with interaction terms in regression that cannot have a negative product?
Assume we have the following model: $y = \beta_0 + \alpha_1 * x_1 ^{\beta_1} + \alpha_2 * x_2^{\beta_2} + \alpha_3 * x_1^{\beta_1} * x_2^{\beta_2}$ where as we have the following priors for our IV's $\...
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Is it appropriate to model a time series by applying a linear regression using the moving average of the predictors?
I have a dataset of football (soccer) data, where for each player in a given season, I have the (fantasy football) points scored in a particular match, the opposition attacking and defensive strength ...
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SEM/regression: Identify better predictor
I have data from a longitudinal study, specifically MRI data and performance on a neuropsychological test at two time points. I would like to test whether the change in gray matter in Brain Region A ...
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Relevance & Exogeneity of IV
I got two questions which are somehow closely related:
Let's take the famous study of Acemoglu et al. (The Colonial Origins of Comparative Development: An Empirical Investigation) as an example.
When ...
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Covariance of slope terms in different linear regression models
I have two linear regression models: one with intercept term, and the other is without. I wanted to compare the models based on their parameters.
MLE estimator for intercept model is well known to be ...
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Marginal means (or "adjusted predictions") with categorical predictors
Goal
My analysis goal is to estimate the expected value of the outcome variable under three different conditions defined by a set of 3 categorical explanatory variables with two levels each. However, ...
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Dealing with 0's in loglog regression by using indicator functions I(x > 0)?
Assume we want to estimate the following model
$y = e^{\beta_0} * x_1^{\beta_1} * x_2{\beta_3}$ which we can linearize into
$\log(y) = \beta_0 + \beta_1 * \log x_1 + \beta_2 * \log x_2$
Assume that ...
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Making and reporting a logistic regression, stratified by sex and age
This question was already asked at Stackoverflow - R Language Collective, but they said this might be a better place to post this question, so here I am.
I'm doing the statistics in R. I have this ...
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loglog regression with 0's in IV's
Assume we have 2 predictors $X_1$ and $X_2$ and an outcome $Y$ that we wish to model with the following function
$y = e^{\beta_0} * X_1 ^{\beta_1} * X_2^{\beta_2}$
Also assume that we have some priors ...
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Aggregating T-statistics and F-statistics across monthly cross-sectional regressions
I am trying to replicate the results in Table V of the paper Individualism and Momentum around the World (2010) by Chui et al. This is attached herewith.
Dataset:
Dependent variable: Monthly returns ...
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1
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Unpack the notation used in Wikipedia's decomposition of the Brier score
Wikipedia has an article about the Brier score whose notation confuses me.
The article starts out easy enough by defining the Brier score to be:
$$
BS = \dfrac{1}{N}\overset{N}{\underset{i = 1}{\sum}}\...
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Orthogonal polynomial contrasts in SPSS (for a binary logistic regression)
I have 4 IVs: gender (male, female), marital status (married, single), threat (continuous variable) and stress with four levels (ranging from 7 to 10 with ten being 'most stressed'). My DV is ...
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Coefficients in linear regressions
Good evening,
I have a question concerning a linear regression. The first picture shows my model and the hypotheses. The second picture shows the linear regression output for H1, H2 and H3. I ...
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How to compare influence of outlier in regression model. ANOVA of two models in R
I am doing linear regression in R. I have identified an outlier in my data:
...
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Best way to set-up a linear mixed model analysis for medical device bench data?
I am working on a bench study comparing two commercial devices (Device X and Device Y) and their ability to hold contact force over 30 seconds on a substrate at 2 independent angles (16 and 130). This ...
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violation of cox proportional hazard assumption
I'm using cox regression to analyse my data. The explanatory variable is a congenital disease (X) and the outcome is an another disease (Y), which is a comorbidity of the congenital disease. I'm ...
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Can the calibration-discrimination decomposition of Brier score be viewed as the bias-variance decomposition of mean squared error?
The mean squared error has a famous decomposition into bias and variance.
$$
\text{MSE} = \text{bias}^2 + \text{var}
$$
Brier score is also a mean squared error calculation, and Brier score has a ...
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Are these two definitions of the coefficient of determination $R^2$ equal?
I want to do multiple linear regression as explained on this Wikipedia site: I am given the following data:
$$
yx=(~(y_1,x_{11},\ldots,x_{1p}),\ldots, (y_n,x_{n1},\ldots,x_{np})~)
$$
of $n$-many ...
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How to Handle Non-Multinormality in the Context of Exploratory Factor Analysis for Logistic Regression
I'm trying to follow the book A Step-by-Step Guide to Exploratory Factor Analysis with R and Rstudio, by Marley W. Watkins, and apply the principles in the book to a real-world data set. Ultimately, ...
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Adaptive piecewise linear regression of empirical distribution function
I need to find the best, in the mean-squared sense, piecewise linear regression of an emprical density function (eCDF, which I do not know but can be sampled online) on the largest possible ...
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Understanding application Lasso and Ridge Regression
Currently reading up on Ridge and Lasso regression, have some questions to clarify.
Suppose Model 1 has all predictors (i.e., 8) and Model 2 only has a specific subset chosen after EDA (i.e., 5)
...
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Log-Level Model Parameter
Consider we have a population regression function (log-level model) with only one independent variable:
$$\log(y) = B_0 + B_1 \times x_1+u$$
In order to find the relationship between the increase of $...
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Why extrapolating a linear model breaks the regression line
When extrapolating a regression line a bit further from the observed range of predictors, I get values way over what seems expected from the fitted model. If the intercept and the slope create a line ...
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Why aren't OLS standard errors becoming smaller in the presence of serial correlation?
I am conducting a Monte Carlo simulation to assess how OLS homoskedastic standard errors (i.e., based on $\sigma^2(X^\prime X)^{-1}$) change as serial correlation changes in a bivariate linear ...
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Correspondence between SAS proc surveyreg and R svyglm [closed]
I am trying to model my proc surveyreg from SAS in R, because their survey package provides an IV option that I intend to use.
<...
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Using Maximum Likelihood function to find near-optimal solution
For the context, I was writing my BSc thesis on the topic of Linear Regression through the Origin (RTO). My goal is to analyze RTO, and find the appropriate use cases for it. In the case of simple ...
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Mixed model with nested and crossed random effects
I'm new to mixed effects models and am trying to use the lmer() function from the lme4 R package to specify a random effects ...
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Specifing random effects in LMM (LME4) for a "beyond optimal model" in a top down driver approach
I'm struggling to set random effects for my linear mixed effect model. I've been trying to go about it using a top down approach in accordance to Zuur et al. (2009), but due to the fact that you have ...
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Fixed Effects causes Multicollinearity
I have a question regarding my regression model and would be grateful for any help.
I have a dataset that contains every tranche of a Deal (a Deal may contain multiple Tranches) and its Variables like ...
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1
answer
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Using a variable as a fixed effect and random effects grouping variable in linear mixed effects model
I am trying to decide what is the right random effects structure for my given experimental design. I've read quite a few of the other posts regarding linear mixed effects models and have come across ...
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Should I remove the intercept when I have one dummy variable that covers all the categories in a categorical variable?
I have a categorical variable that has $4$ categories, and I have two dummy variables, $x_1$ and $x_2$, that cover this categorical variable. The $x_1$ variable has values of only $1$ without any ...
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Interpretation of coefficients in HAR model
I'm performing the HAR model by Corsi. However, I don't quite understand what Corsi means by this in the original paper.
He writes:
It is worth noticing that if we accept the interpretation that ...
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Stata and R giving different results for zero-inflated negative binomial regression [closed]
I know this has technically already been asked here, but it doesn't look like the previous question had a reproducible example. I am having the same problem: Very simple, running a zero-inflated ...
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Multinominal Regression Test
If I have 3 IVs that are categorical/nominal and 1 DV that is categorical/nominal not rank or order, can I run a multinominal regression?
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Interpreation - Log tranformed dependant variable and model with square term of predictor (inverted U)
I am estimating a model of the following form:
log(y) = b1 x + b2 x^2 + b3 log(z1) + b4 z2
This is an econometric model with a focus on the impact of ...
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Mixture of two Poisson distributions
I would like to determine the mixing between two Poisson distribution means. I have $N$ observations that are drawn from two Poisson distributions. Each observation is drawn from one of the two ...
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Regression coefficient before vs. after demeaning X
It is well known that $\beta = (X^{T}X)^{-1}X^{T}Y$ for linear regression. While experimenting with this, I found that $\beta$ (excluding the intercept term) remained the same before and after ...
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Statistical analysis to interpret beta effect size for two different elastic net model
I have two elastic net model and I want to compare their coefficient to say if they have any significant beta effect changes across these two models.
I thought of using Anova but realized since we don'...
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1
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My "lagged consumption" variable accounts for all the variation in my dependent variable
I chose the topic of consumption for my assignment in econometrics. My explanatory variables are interest rate, consumer credit, oil price, disposable income and lagged consumption by 1 year.
Using ...
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Methods for fitting a distribution to regression data
I'm hoping to find a method/algorithm/approach for fitting to a distribution to regression data.
Essentially I have a problem where I have survival data with independent variables, but only cases that ...
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Bonferroni Post-hoc after normality test following a glm()
Experiment Design
Mice belonging to knock-out ($n=7$) and wild-type ($n=6$) had their food intake recorded per hour across a 24 hour period. Within this 24 hour period, the first 12 hours is labelled ...
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biased estimation of variable correlated with endogenous variable
I have the following model:
$
X = \alpha_1 + aZ + \epsilon_1 \\
Y = \alpha_2 + bZ + cX + \epsilon_2
$
Suppose that $Z$ is randomly assigned but $X$ is correlated with the error term $\epsilon_2$, in ...
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Is it better to sample more time points or more replicates at constant sample size?
I would like to analyze my data with a linear regression:
t*k = x
x is my measurement with some error
t is time
I want to fit k as best as I can with the best ...
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