Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables.

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700 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, ...
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1answer
6k views

How to determine weights for WLS regression in R?

I am trying to predict age as a function of a set of DNA methylation markers. These predictors are continuous between 0 and 100. When performing OLS regression, I can see that variance increases with ...
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524 views

Calculate goodness-of-fit (with deviance) to compare averaged models?

I need to compare the goodness of fit of several averaged logistic regression models by calculating the deviance explained. I'm using the MuMIn package in R to ...
5
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0answers
149 views

What are the consequences of not including random effects in a linear model when they should be added?

I am dealing with repeated measures data in which there is clearly reason to incorporate random effects to account for each subject having multiple measurements. A mixed effects model using random ...
5
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2answers
72 views

Squeezing the juice from a large data set

I may soon have temporary access to a large and interesting data set, where the data is sensitive and raises privacy and confidentiality concerns. Number of records in the low hundred thousands, ...
5
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3k views

Is it possible to do a time series analysis with more than one explanatory variable?

I am working on a project, and I am absolutely new to forecasting and not so strong in statistics. I have an employee data for the last 7 years, along with the other variables like economic growth, ...
5
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216 views

Variance partitioning - why be cautious?

I'm about to use variance partitioning to interpret my results of a given model and across models and have come across various criticisms of it most notably by Pedhazur (1982, 1997). Also, the ...
5
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1answer
2k views

Comparing observed and predicted values across several measurements

As a neuropsychology graduate student with some experience in statistics (I'm usually the guy other psychologists come to with statistics problems after trying it themselves but before seeing a ...
5
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2k views

Why is correlation between y and $\hat{y}$ in a model with and without intercept equal?

I consider a very simple example with two models like this; ...
4
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32 views

Before using CV-selected Regression model for Inference, shouldn't model performance be evaluated on unused test set?

I just came across a biokinesiology paper that used some Machine Learning methods, but I think there is a flaw in their methodology. The authors had data on stroke patients and used Lasso regression ...
4
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71 views

using `lmer` to fit the linear mixed effects models

Edit: I know some people vote this question is off-topic since it is more like a Cross Validated question. However, I am not here to ask about the coding thing (but I might word in the wrong way). I ...
4
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0answers
129 views

Predicted R squared

When calculating the predicted $R^2$ value for a linear model using the equation $R^2 = 1 - \frac{PRESS}{TSS}$ should the currently left out sample also be excluded when working out the mean value ...
4
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142 views

Why shouldn't I standardize my predictors when putting them into a regression model?

There are multiple reasons for applying standardisation/mean centre for predictors before putting them into a regression model. However, in the literature, some people do not do so or even argue ...
4
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360 views

How to visualize models after multiple imputations by chained equations

I'm starting to prefer visualizations of my regression models as opposed to tabular output (OR's, beta-coefficients, 95%CIs). However, I struggle to find a good way to do this when I am undertaking ...
4
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188 views

How can I find and categorise the effect size of a single coefficient in a multiple regression?

Question How do I find the effect size for the different hierarchical multiple-level regressions used by papers in my review? And how do I categorise their effect size? Detail I’m publishing a ...
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496 views

Benchmark priors for Bayesian ridge regression

Consider a Bayesian linear regression model $$\mathbf{Y=X\beta} + \boldsymbol{\varepsilon}$$ where $\mathbf{Y} \in \mathbb{R}^n$ and $\mathbf{X} \in \mathbb{R}^{n,p}$ are given, $\boldsymbol{\...
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74 views

Ill-behaved, nonnormal residuals of multiple regression: should I be concerned?

I have data on waist circumference (cm) (waist), gender, age and physical activity (vigorous MET minutes per week) (PA). I was trying to run linear regression in R on the model waist ~ gender + age + ...
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143 views

Continuous distributions as independent variable in regression

Problem: My research issue concerns logistic regression where each observation is an area, not a simple point. As such, each independent variable ($x_i$ of $\boldsymbol{X}$) is a distribution of ...
4
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246 views

Connecting Poisson and multinomial models

Let's say we have multinomial counts $y_{jp}$ (corresponding to observations $j$ over categories $p=1,...P$) that are arranged in a table of $n$ rows and $P$ columns. Then say we have the log-linear ...
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4k views

Zero-inflated model: non-finite value supplied by optim

So I have the following model predicting the presence of an animal on a certain spot. As a time unit quarter is initially used, but for one of the species of animals there is some (little) interesting ...
4
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90 views

Testing differences between slopes by examining proportions rather than interactions

In a recent article published in Nature Genetics, Francioli et al. argue that the relationship between paternal age and mutation rate depends on what part of the genome you're looking at (intergenic ...
4
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0answers
799 views

Coefficients of dummy variables in multiple regression

I am struggling with interpreting coefficients from a multiple regression analysis with multiple categorical (dummy) variables. I am running a linear mixed model with biodiversity (...
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0answers
956 views

Analysis of Multiple Time Series Data with Exogenous Shocks

Real Life ProblemThis one is a tough one and some crowd sourcing seems like a good way to get some feedback. I am trying to determine the effect of Non-Farm Payroll surprises on a subsector of the ...
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573 views

Longitudinal data analysis where meaning and metric of response variable varies over time

Determining what factors predict change over time is a topic of investigation in many fields and there are a variety of readily implemented methods for analysing repeated measures in the same metric. ...
4
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2k views

VAR model for price forecasting in multiple time-series context. How to get “real figures” as forecasts?

Sorry for the rather long introduction, but since I was (legitimately) critizised for not explaining my cause and questions enough, I will do so now. I would like to conduct a (price)-forecast based ...
4
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0answers
361 views

Partial regression plots vs scatter plots for checking linearity

In a multiple linear regression analysis, what is the most suitable plot for checking linearity? I have seen a number of examples that use scatterplots as a preliminary test to use a linear model. But,...
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375 views

When including a linear interaction between two continuous predictors, should one generally also include quadratic predictors?

Suppose I am fitting a linear model, and I have two continuous predictors x1 and x2. I think that they might interact, so I add ...
4
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0answers
493 views

Standardize continuous predictor variables on [0, 1] scale?

I'm working on a health care regression model predicting # of inpatient visits. My analysis dataset includes a number of hybrid continuous/categorical predictor variables which can hold values on a 0 ...
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738 views

Assumption violations with heteroscedastic data and OLS regression

I'm trying to model the typical performance of an experimental approach I've developed. I have a total of 3000 observations for 72 different case studies. My observations consist of a reading for <...
4
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0answers
9k views

Fitting a zero-inflated negative binomial regression with R

In this thread, I laid out a problem involving fitting a model that attempts to use minor league baseball statistics to predict success at the major league level (explained in full in the thread). ...
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0answers
2k views

How to do a multiple regression with ARIMA using R?

I am analyzing some tree physiology data (transpiration) in relation to a number of environmental variables (many of which are predictors such as temperature, PAR and vapour pressure deficit). I ...
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0answers
185 views

Relationship between LASSO T and LARS number of steps k

We can see on the figure (cf Least Angle Regression p30, Efron, Hastie, Johnstone, Tibshirani - link: Least Angle Regression) that there is a direct relationship between: LASSO T absolute norm of $\...
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1k views

Hierarchical regression with dummy variables

I need to perform hierarchical regression with dummy variables. I also need to check moderation by introducing in the model interactions of these dummy variables and the moderator. My questions are: ...
4
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1answer
458 views

Fitting a particular Gaussian model

Using R or SAS, I want to fit the following Gaussian model: $$ \begin{pmatrix} y_{1j1} \\ y_{1j2} \\ y_{1j3} \\ y_{2j1} \\ y_{2j2} \\ y_{2j3} \end{pmatrix} \sim_{\text{i.i.d.}} {\cal N} \left(...
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27 views

AIC and model selection with multimodel

For a simple example, I am doing a multi-model regression/likelihood estimation. The data is $(y_1,y_2,x_1,x_2,x_3,x_4,x_5)$. The first model (A) consists with two regressions: $y_1=e^{a_1x_1}+e^{...
3
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1answer
18 views

In linear regression, what is the difference between performing variable selection before assessing multicollinearity or vice versa?

If you have a number of variables you're interested in and want to perform linear regression, is there a clear preference between: Method A. Perform variable selection techniques (e.g. using ...
3
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1answer
47 views

Standard error in multiple regression

I want to calculate standard error of y-intercept or constant term in the multiple regression equation $Y = b_0 + b_1X_1 + b_2X_2$ I found the formula for standard error estimation of co-efficient $...
3
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15 views

Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to my regression model?

Lots of people seem to be asking this. They often seem to get shallow answers that merely assert what is true, instead of drawing or explaining the mechanism. They also seem to not find each other -- ...
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0answers
25 views

How to account for error in measurement of dependent variable in prediction interval (in multiple regression)?

I am trying to figure out the best way to take into account known measurement error in the Y (dependent) variable when producing prediction intervals from a multiple regression. I have the standard ...
3
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0answers
57 views

How to prove an OLS estimator is inconsistent

I have two equations $Y_i = \beta_0 + \beta_1X_i + \epsilon_i$ $X_i = Y_i + Z_i$ and additional information that $cov(\epsilon_i, Z_i) = 0$ And I need to prove that using the OLS in the first ...
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0answers
17 views

Multiple regression for left-censored independent and dependent variables

I am interested in developing a predictive multiple regression model which predicts a concentration of one compound based on the measured concentrations of several other compounds. Both the dependent ...
3
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1answer
80 views

multiple regression with constraints of independent variables

I'm running a regression analysis with independent variables $X_{1}, X_{2}, \cdots, X_{n}$ and dependent variable $Y$. There is a constraint among some of the independent variables, say, $X_{1} + X_{2}...
3
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35 views

What are the differences between HC estimators and their small sample properties?

I am currently using R to run regression with the following code: ...
3
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0answers
24 views

Compare slopes between two groups of equal size

I want to compare how does a dependent variable (total flow) changes with a covariate (total rain) between two groups (stream A & B). Usually, i would go with ANCOVA. But these groups have the ...
3
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0answers
48 views

The minimal possible value of total sum of squares for linear regression

I have a regression model $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 +u$ It is known that sample means of both $x_1$ and $x_2$ are zero, moreover the error term is said to be homoskedastic, the ...
3
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0answers
47 views

A simulation study of linear mixed model

I am reading this paper, a note on BIC in mixed effects models, and I was trying to repeat their simulation study. And I will paste part of the experiment settings here to clarify my question. Now, I ...
3
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0answers
36 views

regression analysis with both slope and value data

I have measured data $\{x_i, y_i, y'_i\}$, to which I would like to fit a polynomial $y=a x^2 + bx + c$ and $y' = 2ax + b$. It occurs to me that the regression problem of fitting $y=a x^2 + bx +c$ to ...
3
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1answer
44 views

Importance of regressors in time series data

Could anyone recommend bibliography or name some useful methods to analyze which (exogenous) variables are most important in determining the value of a time series? For context, I have a random time ...
3
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0answers
86 views

Time-series: Using decomposed components (seasonality+trend) as covariates in multiple regression?

I need to evaluate the effects of a treatment on a time-series data-set by comparing multiple dependent variables to a prior time period without treatment in effect. I'm using a python library to ...
3
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0answers
892 views

Difference between suppressor variable and multicollinearity

I have having trouble understanding the difference between a suppressor variable and multicollinearity in multiple regression. If a suppressor variable is one that is not correlated to the outcome, ...

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