Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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Slope / regression slope value of a non-linear line [closed]

Slope of a line given multiple points Hello, I came across a closed question, but what I really don't understand is the formula being used - what is this formula (any authoritative references)? From ...
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Stata: Difference-in-Difference model with time variant treatment?

I want to measure the effect that a treatment (merger) has on firms (y). Therefore, I have panel-data for 6 years (2010-2015), consisting of about 1,500 firms. There are 100 firms that are somehow ...
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Get a range of values (val_1 to val_2) instead of one value in linear regression

So, the idea is that I use linear regression and I get an equation y = a * x + b. So when I give a value x I get a predicted ...
4 votes
1 answer
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Why Do Residuals Need To Be Homoscedastic (Equal Variance)?

I am MBA student and am taking a course on "Research Methods" - in this class, we are learning how to perform basic statistical analysis such as Hypothesis Testing and Regression Models. Our ...
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1 answer
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Is there something equivalent to a ROC curve for logistic GLMMs? [closed]

When I read previously about logistic regression, I recall some talk about ROC curves and how they can be good metrics for the sensitivity/specificity of a logistic regression as well as a goodness of ...
1 vote
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Biased Parameter Estimation in Poisson Regression

I read over here (https://aip.scitation.org/doi/pdf/10.1063/5.0040330) that "If the equi-dispersion is not met, the Poisson Regression is no longer appropriate to model the data. Moreover, the ...
1 vote
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Is there a multilinear principal component regression?

PCR is a linear regression problem on top of PCA. Analogically, is there a 'multilinear PCR' as a linear or multilinear regression problem (e.g. CP tensor regression and Tucker tensor regression for ...
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Which groups are reference groups in a regression model with interaction?

What are the reference groups in a regression model where there are interaction categories? Using the iris dataset in R, I've created a category with three levels ...
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What kind of residuals should we test for linear mixed-effects models (LMER)?

I'm on a journey trying to get my mind around the normality of residuals assumption for linear mixed-effects models, this is a FOLLOW-UP POST While studying to better understand what I could do to ...
1 vote
1 answer
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Regression Analysis of Time as Independent Variable in Experiment

we conducted an experiment on a sample of 30 persons. For every person, we observed the outcome variable every 15 minutes, so for each person 10 times. IV: Time (in Minutes) DV: Interval Scale [1;9] n ...
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Does Frisch–Waugh–Lovell theorem work on panel data?

We consider the following panel regression model \begin{align} Y_{i} = X_{1,i}\beta_1 + X_{2,i}\beta_2 + \epsilon_{i} , \ i=1,...,N, \end{align} where $Y_i := [y_{i1},...,y_{iT}]'$, $X_{k,i}:= [x_{k,...
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algorithm to either fit data as linear or stepwise constant

Given data $(y_i, x_i)_{i=1}^n$, I wish to fit either: a linear regression, $y = \beta_0 + \beta_1 x$; or a stepwise constant function, $y = \left\{ \begin{align} y_1 & \text{ if } x &...
1 vote
1 answer
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Elastic Net Collinearity

When performing linear regression it is often assumed that the predictors are independent with Gaussian noise: \begin{equation} Y = X\beta + \epsilon \quad \epsilon \sim \mathcal{N}(0, \sigma) \end{...
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Question About Overdispersion and Poisson Regression [duplicate]

I am an MBA student and taking some classes in statistics - I have taken a few basic stats classes where we learned about the fundamentals of statistics and probability. We started learning about ...
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Probit Model When Dependent and Independent Variable Binary

I am running a Linear Probability Model with a binary dependent variable and a binary independent variable of interest. Additionally, I include control variables that can be binary but also continuos ...
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Interpreting the time series linear regression - differences before and after collapsing data

Consider the following time series: The coefficient on the linear regression makes sense: each additional year, the variable Y increases by 3 percentage points. Now, the problem occurs when I'm ...
2 votes
1 answer
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simple slope analysis for curvilinear mixed model

I am a student currently working on a simple slope for mixed model and came upon a question. As I am interested in a two-way interaction that involves a quadratic term of X variable and a moderator, I ...
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2 answers
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Why Specifically Use Poisson Regression For Count Data?

I am a MBA Student that is taking some statistics courses, a colleague recommended this site as a useful resource! So far there seems to be a lot of interesting information here! I posted a previous ...
1 vote
0 answers
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dependent observations for logistic regression [closed]

I am trying to set up a logistic regression model for inventory units and sales. My binary response variable (sales) is 1 if overall sales are up over last year and 0 if they are not. I have about 30 ...
2 votes
2 answers
42 views

Why do sampled functions from a Gaussian Process perfectly interpolate the data?

I've been studying GPs with Rasmussens book as well as a few of my old probability favorites. I am confused by the results we're getting (doing also a lot of practice) when sampling from our Gaussian ...
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How to interpret mixed level logistic regression with contrast coding?

I'm currently trying to interpret several mixed-level logistic regressions with contrast coding and it is my first time using this method. My main research of interest is the intercept, which is ...
1 vote
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Question on "Count Regression"? [closed]

I am a MBA Student that is taking some statistics courses, a colleague recommended this site as a useful resource! So far there seems to be a lot of interesting information here! We are learning about ...
2 votes
2 answers
36 views

Questions on the Wishart distribution

If $X$ is an $n\times p$ matrix where each row is iid multivariate normal, then $X^TX$ has a Wishart distribution. What is known about the limiting distribution of $X^TX$ for large $n$ when the rows ...
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What exactly are you plotting for each lag value when calculating the correlations for a PACF?

I understand this for an ACF plot. You are plotting $x_t$ vs $x_{t-1}$ and then calculating $r$. This gives the point $(1, r_1)$. Repeat for lag 2: plotting $x_t$ vs $x_{t-2}$ and then calculating $...
3 votes
1 answer
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compare model fit logistic regression negative two times log likelihood

I'm trying to decide between two logistic regression models. I think I've used the negative two times log likelihood criterion before. My two models are not nested - can I still use that approach? ...
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3 votes
1 answer
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What does "1-unit change" mean when centering predictors in regression?

I know that when we standardize a predictor, "one unit change" becomes one standard deviation in the predictor, but what if we only center the data on the mean (i.e. only subtract all values ...
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Measuring the effect of variables on the variance of a dependent variable

Say we have a model with three predictors and one dependent variable. For the sake of our example let the model be the following: Y = X1 + X2 + X3 + e Where Y is a 1-10 feeling towards apples, and X1, ...
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How to calculate a financial beta and theta (time decay) in R linear regression?

I have the following code trying to calculate a beta (if priceA goes up 1, then priceY goes up X) and theta (each month that passes priceY goes down Z). ...
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is there a way to obtain difference between two estimates with confidence intervals?

I am using time-based regression to estimate an effect of an intervention. I have two separate hypothesis: H1A: the intervention will have a positive effect on one time series a1. H1B: the ...
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To include or not the event indicator in modeling probability of treatment censoring

Setup In observational studies, inverse probability of censoring weights (IPCW) can be used to adjust for informative loss to follow-up or in the context of non-compliance, treatment switching. I'm ...
1 vote
1 answer
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hierarchical regression models interpretation (with interaction term)

I am running multiple regression to test my hypothesis, which includes interaction terms. I have some control variables and three key predictors A, B and C. I used hierarchical regression models which ...
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Coefficients of the regression line of observed vs predicted data for a model - assumptions and proof

This 2008 paper by Piñeiro et al. shows that the 'correct' way to represent the relationship between a model's predicted values (P) and the observed (experimental) values (O) that originated it is to ...
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Regression coefficients with different signs (one positive, one negative) in a mediation analysis

I ran a mediation analysis following this article (which goes over the Baron & Kenny method). Step 1. lm(Y ~ X, data); My X (independent) variable has a significant relationship with my Y (...
1 vote
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Compound distribution regression vs random effect model

What is the difference between a regression model with a compound error distribution (e.g. negative binomial, beta binomial) and a binomial/poison GLM with a random intercept (say Gaussian)? Is it ...
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Is it correct to use $R^2$ as an accuracy measure for an xgboost model in time series forecasting? [duplicate]

I am trying to evaluate time series forecasts in terms of accuracy. For example, I want to be able to say that the model "X" is x% accurate. In the litterature all metrics are errors such as ...
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Generalized Linear Model (GLM) in Python

Say that my data consists of time success failure exog 2009 3 1002 0.2 2010 2 1200 0.3 2011 9 1091 0.1 2012 0 1099 0.4 And I want to fit a GLM with a Binomial family and Logit link to this ...
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2 votes
1 answer
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Aggregated time series or regression approach?

The setup I describe below is analogous to my actual problem. Problem: I have millions of individuals in my dataset and for each individual, I have certain stats over time. I.e. for one individual Joe,...
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Compare conditional effects (simple slope) from regression model

I have the following regression outputs from a model that includes both quadratic and cubic interaction terms. I calculated the simple slopes using the simle_slope from reghelper. ...
2 votes
1 answer
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Interpreting plot of interaction effects

In this vignette, the plot_model function is described and some examples are given on how to plot two way interactions along with confidence bands. I am wondering how to bets interpret such plots. For ...
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2 votes
1 answer
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Negative correlation in two groups (separately) but overall data shows positive correlation

Regression on the overall data gives positive correlation coefficient. However, if I divide the data by gender (male and female) and run the same regression model separately on each group - I get ...
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2 votes
1 answer
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How to establish relationship between regressions on subsets of data?

From classical OLS, the regression of $y\in\mathbb{R}^n$ on $X\in\mathbb{R}^{n\times k}$ yields $\beta = (X^TX)^{-1} X^Ty$. Suppose we were to partition $X$ into two blocks as: $X = \begin{pmatrix} ...
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Can you use two stage least squares (instruments) on an endogenous categorical variable (Likert scale)?

I have an endogenous categorical variable (exlanatory variable) measured on a Likert scale (from 1-4) and I would like to instrument it via 2sls. I am wondering if this is a theoretically correct ...
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Meta analysis for a number of identical studies (with access to raw data)

I have access to about ten almost identical studies from ten different locations. They have been done different years, but with the same methodology. Each site was analysed and reported separately ...
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Forecasting model to categorize promotions - do I need one or two forecasting methods, one for prediction and one for inference?

I have a project where I'm trying to do two things: Create a forecast for sales Categorize the value for promotions The data has a weekly seasonality, but it's a totally irregular seasonality. I ...
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1 answer
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Explaining importance of interaction that is statistically insigificant

Consider the following dataset composed of two different groups blue and red which are observed over time. The super-imposed lines are regression lines fit to each group separately, i.e. for each ...
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1 vote
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Is it possible to do linear regression on participants' level?

Each participant had 16 rating values, and there were two (say A and B) trial-wise parameters I could get based on our task. I want to see how A/B contribute to the rating for each subject. Is there ...
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2 votes
1 answer
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How do I calculate weights for weighted means?

I want the weighted mean of my dv, velocity. In this scenario, velocity is a derived/interpolated measure comprised of repeated measures of randomly sampled speeds in a given region. There will always ...
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Sign change of coefficient in logistic regression when change from binomial to continuous predictor

I am looking at the association between the application of animal control and population reduction. Population reduction is my outcome variable; it is a binomial variable where 1 = population ...
1 vote
1 answer
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RMSE and R2 with different training splits

I am running 2 linear regression models using the same data with different data splits. n=205 70/30 split RMSE: 2341 R2: 0.85 50/50 split RMSE: 2474 R2: 0.88 Seems counterintuitive that the R2 ...
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How to compare different subsamples in mixed logit model?

When conducting a discrete choice experiment, we additionally split the sample randomly in a control and treatment group testing one specific effect and would like to now examine whether the treatment ...
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