# Questions tagged [regression]

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

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### Weighted least squares vs log transform

I'm sure that I'm going to get somebody annoyed by my lack of research on this question, but I'm not good enough at statistics to know where to go to do the research effectively, so please try to bear ...
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### What model or method to use for categorical data with repeated measures?

I am trying to analyze my data, it consists of 2 independent categorical variables (4 textures and 4 impact sounds - mixing and matching them gives me 16 different conditions that each person is shown)...
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### Change score as predictor

I want to see if a change in an independent variable (T2-T1) predicts another variable at T2. For example, higher increases in cognitive impairment over 1 year for people with dementia predict lower ...
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### Coupled Multivariate Regression and AR(1) Process for the Covariates

I am wondering how to fit the following model: I have a standard multivariate regression, and a set of covariates X. I want to couple my regression equation with an AR(1) process for the dynamics of ...
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### Can I use the Estimate of a model directly without considering the p-value?

this is a follow-up question of (this question). The research question is to get the intraindividual (within-subject) variations on contact patterns per period. Each participant reports their contact ...
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### Why different results for linear regression in sem() from lavaan and lm()?

thanks for reading this. I am a student trying to understand more about statistics for social science questions. I am trying to build equivalence in R between the sem() function in {lavvan} and the lm(...
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### Modeling Transitive Preference

I've conducted a preference test twice on 10 subjects, presenting them with three options in all six pairwise combinations (AB, BA, CB, BC, AC, CA). I need to determine the following: if each subject ...
1 vote
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### What statistical method to use for binary independent variable and continuous dependent variable

I have a dataset that has columns item, week, and units sold. I have another dataset that has columns group, week, and flag. The weeks for both datasets lie in the same range. Units sold is continuous ...
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### Mixed effects models with only categorical data?

This is my first time trying to run any type of mixed effects models. I have a dataset where I was instructed to use some form of mixed effect modeling (lme4 package) to see if functional traits of my ...
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### Multivariate analyses using mixed models vs. other approaches

Multivariate analyses (i.e. several dependant variables) can be performed using mixed effects models. In brief, columns representing the dependent variables are stacked on top of one another into a ...
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### Between two variables with weak correlations and no significant prediction rate from simple regression, what are the next research steps?

I am working to determine the association between crime rates and economic inequality using income brackets. I have found that some crime rates are weakly, or almost moderately, correlated with rates ...
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### logistic regression: categorical predictor with many levels - appropriate group sizes

I'm estimating a logistic regression model with a categorical predictor with 11 groups. I'm wondering whether I can/should exclude some of these groups (D-K, maybe C as well; see below) b/c of small n ...
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### Prediction of a time series AR(1) vs AR(1) with exogenous variables vs Random Forest, why is the performance so different?

Extension of the previous question that only compare AR(1) vs. AR(1) with exogenous variables: I am currently working on forecasting a time series y using three models: an AR(1) model and an AR(1) ...
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### Using a Response Variable as a Predictor Variable in a Future Model?

This is a statistical problem I am working on and I would like to request some guidance from the respected community. Suppose there is a factory that receives food orders. The food sits in a ...
1 vote
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### Given a predictor $x$. under what circumstance would you have high $R^2$ but low $\beta$

Assume I have a time series $y$ and a predictor $x$. Let's say they are both centered at zero. $$R^2 = 1 - \frac{ \sum (y_i - x_i)^2 }{\sum y_i^2}$$ Now I run a new regression $y \sim \beta x$, in an ...
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### Rule of Thumb for Mixed Model

Suppose that we have $n$ observations of $(X,Y)$ pair, where $X$ are real (might be vectors), and $Y$ is real. We want to a linear model. One rule of thumb is that the number of learnable parameters ...
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### AR(1) model predictions: Are the predictions shifted by one period?

I am estimating AR(1) one step ahead forecasts for the following data using the following code. The AR(1) predictions seem to perform quite well. However, they seem to be shifted by one period in to ...
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### How does SYSTEMFIT from R work (from statistical perspective)?

In R, there is a package for estimating systems of equations with OLS, called systemfit. Initially, this package does not seem to add that much of a value, as I can ...
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### Multicollinearity when controlling for a variable

I have a few questions about multicollinearity in my data: I'm looking at a certain type of lesion seen on MRI scans; for each patient I know the volume of those lesions and a metric that captures the ...
298 views

### Linear regression model building: Do I need to include variables previously proven significant to a model?

for a school project for an introduction course to linear regression we need to analyze three research questions: Does fertiliser type affect corn yield? (Yield ~ Fertiliser) Does corn variety affect ...
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Consider the classical measurement error model: $$Y= \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \varepsilon$$ where $W=X+U$ is observed. X is the 'true' quantity and U is the measurement error. Var$(X) = \... 3 votes 2 answers 60 views ### Justifying a linear model I am interested in the association between two variables, cognitive distortion and overall suffering (on scales from 0 to 40 and 0 to 10 respectively). A Spearman rank test suggests positive ... • 43 1 vote 1 answer 35 views ### When is omitted variable bias non-zero? I was just reading the Wikipedia page on omitted variable bias: [wiki for OVB][1], and I was confused by one of the main claims of the page, which is that the expected omitted variable bias is 0 iff ... • 408 2 votes 1 answer 122 views ### What analysis is best with a binary independent variable that is very skewed? I have a binary independent variable (1 = event occurs, 0 = no event occurs) and a continuous moderating variable. My dependent variables are continuous. I want to test if engaging in a particular ... • 23 -1 votes 0 answers 14 views ### Unbalanced panel data - best options? I have a set of house purchase transactions for the years 1920-1935. I am hoping to examine the effect of a range of variables on the size of these transactions. These transactions often involved the ... 0 votes 1 answer 22 views ### Outlier detection for data set comparison I have two data sets with similar columns, one numerical and the rest categorical. col_1= categorical: city_name, col_2= categorical: company_name, col_3 = categorical: product_name, col_4 = numerical ... 1 vote 1 answer 23 views ### How interpret contrary coefficient estimates in a logistic regression? I need help to interpret a result output of a mediation analysis. I have a predictor X that predicts three mediators variables M1, M2, M3 in a negative way. When X increases M1, M2, M3 decreases. M1, ... • 41 0 votes 0 answers 22 views ### Mixed signs of coefficient in mediation - what does that mean in fact? I have an interpretation problem that I have not been able to solve using any of the books I have found on mediation. I understand many aspects of it, but the model in which the signs are mixed up ... • 293 2 votes 1 answer 143 views ### How to interpret sum of z-scores and average sum of z-scores? Suppose I have data from 5 sub-tests and 2 groups of participants. What is the difference in the interpretation of a sum of z-scores (i.e, transform all 5 measures into z-scores and sum them up) ... • 803 0 votes 0 answers 21 views ### lm in non-full rank case [duplicate] MATHEMATICALLY, how does lm deal with the case when the data is not full rank? Take the simple example : ... • 512 1 vote 1 answer 66 views ### Weighted least squares, checking normality Assuming I want to perform a linear regression, I can do: ... • 51 0 votes 0 answers 17 views ### Model performing poorly after cross validation After using cross-validation to see how a custom predictive function performs on unseen data, I applied to function to the original dataset, and the performance (based on coefficient of determination) ... 4 votes 2 answers 174 views ### Compare estimates between non-nested mixed-effects models I have two mixed-effect linear regression models, both fit on the same same data and same outcome, but with slightly different predictors. Is there a way to compare (i.e., generate a p-value for the ... • 1,679 0 votes 3 answers 100 views ### Regression with a 0-1 variable. Should be the same as running a t-test, but I get a different p-value [duplicate] I have a dataset in R where I have volatility estimates (in my case, just standard deviation of minute returns on that day) for different days: ... 1 vote 1 answer 29 views ### Type of model to measure spread between two assets I am analyzing the price between two assets and the relationship between various features that impact them. The vast majority of the time, over$90%$, the assets are equally valued, thus the spread is ... • 161 3 votes 3 answers 208 views ### Regression and independent random vectors Lets consider that data samples are generated from random vectors$(X_1, Y_1)...(X_N, Y_N)$of cross-sectional data. For regression one usually assumes that the error distribution is I.I.D. normally ... • 143 6 votes 1 answer 105 views ### Isn't it normal that residual plots for mixed effect models will show a trend? Whenever we include a random effect in a mixed model, since the estimates are shrunk, isn't it normal at the fundamental level that the residual plot will show a positive correlation between fitted ... • 93 0 votes 0 answers 24 views ### When working with real life data, how do you handle many missing/NAs in columns for modelling? [duplicate] I'm kind of a newbie in this regard and having trouble understanding or how to deal with it. I work with a lot of patient data and this data comes from nurses/doctors about how patients are treated. I ... • 11 2 votes 1 answer 58 views ### Linear model with interaction - pairwise comparison I have the following model in R: lme(log_weight ~ log_weight0 + Group*Day, random = ~ 1 | ID, data = mydata) The interaction term is significant. I would like to ... • 85 -1 votes 0 answers 11 views ### Convergence of logistic regressor in infinite data limit I am reading through the paper "Nonlinear ICA of Temporally Dependent Stationary Sources" (Hyvarinen 2019), which cites the following "well-known" result for two-class logistic ... 0 votes 0 answers 11 views ### Goodness of Fit for Comparing Multiple Fractional Logit Models I'd like to use employ a fractional logit model where my dependent variable is bounded between 0 and 1 and I have two independent variables. For this type of model, I'm unsure, and hoping to get some ... 0 votes 0 answers 27 views ### Appropriate coding for bipolar Likert scale [closed] For one of my variables, I am measuring affect on a bipolar Likert scale. The question is "how do you feel about the activity?" The range of responses is Worried slightly worried neutral ... • 31 0 votes 0 answers 32 views ### Does it make sense to include both age and birth year as covariates in a model? A researcher asked me about adjusting for both age and birth year in a model. To my mind these are perfectly collinear, but then it got me started looking around online and down the rabbit hole of age-... • 823 0 votes 0 answers 29 views ### Calculate variance of a prediction for TLS Definitions I have a set of data. Let's assume the true underlying model to be$\eta_i=\beta_0+\beta_1\zeta_i$. Where$\beta_i$are the true coefficients of the model,$\eta_i$are the true ... • 135 1 vote 1 answer 71 views ### How to transform my variables before fitting into linear regression? I have a game where there are 4 different types of berries to collect, and I am trying to understand how the collection of each of these berries would influence each other. I made kde plots for the ... 0 votes 1 answer 46 views ### How to estimate the variance of the regression coefficients via Variance-Covariance Matrix? everyone I am not used to the matrix algebra. I know the maximum likelihood method to get the point estimation of the regression coefficients well. However, I don't understand the mathematical method ... -1 votes 1 answer 53 views ### Usefulness of p-value to flag outliers in a data set [closed] Suppose I have a set of data such that $$y= a\times x + b + \varepsilon$$ I am trying to find$a$and$b$, but some$y$'s are outliers and up to 80% of the data is missing, so I don't have access to$...
Assume we have the following linear model $$Y = X\beta + \varepsilon$$ It is well known that the distribution of the residual sum of squares has $\chi^{2}_{n-k-2}$, where $k$ is the number of ...