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Questions tagged [regression-coefficients]

The parameters of a regression model. Most commonly, the values by which the independent variables will be multiplied to get the predicted value of the dependent variable.

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Can I calculate Cohen's $d$ from multiple regression coefficient?

Question: Is it appropriate to calculate Cohen's $d$ (effect size) from the regression coefficient of an independent categorical variable? Background: My regression coefficient represents ...
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223 views

Are these negative binomial regression results reasonable?

I did a negative binomial regression on a data set with 4 covariables. The count outcome has values up to 600. I did a mixture model with 2 components, also called a latent class model. However, I am ...
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170 views

R bayesglm: Estimates depends on order of variable

I did a logistic regression with bayesglm from package arm. I got different results depending on the order of the variables in the model: ...
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236 views

Cross model comparison of quantile regression coefficients

I am looking for a way to compare coefficients obtained from quantile regression. The two surveyed models are nested, estimated on the same sample and for the same quantile. $$ Y = \beta_1X+\epsilon_2\...
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48 views

Confidence interval for the increase in P(Y=1) from moving between 2 levels of a factor in logistic regression

I have a logistic regression model fit with one categorical variable $x$ that takes value in $\{1,2,3,4,5\}$. In R I have obtained the estimate and standard error for $\beta_0$ and $\beta_1$. The ...
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Efficient ways to partition rows of augmented design matrix $[X|y]$ into subsets with similar regression results?

Imagine I have $n$ observations on a regression model; are there any reasonably efficient methods for partitioning that into two (or more) roughly equally sized groups which almost reproduce the ...
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768 views

SARIMA, coefficients check

I would appreciate if someone could check the mathematical equation for the seasonal ARIMA (4,1,4) x (1,1,1) period 12 that I wrote. I have done it this way, but I am not really sure if it correct is. ...
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559 views

Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across hospitals....
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Backing out the standard deviation from information on baseline mean/s.d., and coefficient mean/s.d

I am trying to run a power calculation for a randomized control trial. For this I need a mean and standard deviation for our 'baseline'. There are papers out there which would have a mean and standard ...
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79 views

Decomposing R^2 into independent variables

Consider a linear regression model: $$y = β_0 + β_1X_1 + β_2X_2 + ... + β_kX_k + ε$$ where $R^2 = 1 - (SSR/SST)$. I would like to determine the contribution of a factor $i$ (call it $R^2_i$) into ...
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396 views

Interpretation of Elastic Net Regression Coefficients

I would like to interprete the coefficients of a elastic net regression (i'm using function glmnet()$beta in R). The coefficients of the elastic net regularized ...
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Is Omitted Variable Bias Always Bad? What are the implications of omitting variables from a regression that aren't easily obtained in the real-world?

Say I'm using multiple logistic regression to help caterers in a large city predict the probability invited adults will come to a wedding. Say I have a proprietary dataset of likely relevant predictor ...
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53 views

Find Feature Weighting in Deep Learning

If I train a deep neural network on standard tabular data (csv file etc. with labeled features) is there a good way to gauge how important each feature is in a particular new instance's prediction ...
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327 views

Multinomial Logistic Regreesion with Lasso penalty in R

I am applying regularized logistic regression (in R) to the handwritten digits data set. I have fitted a logistic multinomial model with lasso penalty to the training data. I am asked to obtain the ...
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413 views

What is the covariance between estimated coefficient of a regression model?

Consider the simple linear regression model: \begin{align} Y_i &= \beta_1 + \beta_2X_i + u_i \\ \hat{Y}_i &= b_1 + b_2X_i \end{align} (a) Show that the regression line always passes ...
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537 views

Can autoregressive coefficient values be greater than 1?

I am using multivariate autoregressive (MAR) models to fit my long-term dataset of species abundances and environmental variables but when I use only the data from a specific period of the year (e.g.,...
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4k views

R2 SCORE. Scikit Learn vs StatsModels

I have the next code (and question): ...
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469 views

What explains the correlation between the slope and intercept?

If $R^2$ explains the variation explained by a model, what explains the correlation between the coefficients given for a slope parameter and an intercept? I have been thinking of it in two ways: If ...
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3k views

Obtaining significance for variables in a linear discriminant function analysis

I have run a linear discriminant function analysis using the lda() function in the MASS library to determine which of 6 ...
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3k views

How to determine the significance of an interaction?

My question is simple: How do you determine the overall significance of an interaction (i.e. the marginal effect of $X$ on $Y$ for different values of $Z$)? But the background is a bit long-winded,...
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407 views

Finding standard error of beta coefficients in ridge regression using lambda

I need to get the standard errors of coefficients with Ridge Regression, by calculating the SE of the beta estimates after I choose the right lambda. ...
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509 views

Normality violations in multiple regression - report bootstrapped CIs, p values & t values?

I have analysed some data for a research project using multiple linear regression. However, normality assumptions for this method were not met in my data (and could not be resolved using ...
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2k views

Comparing nonlinear regression coefficients from independent datasets

I performed enzyme kinetics experiments on a three independent preparations of an enzyme and produced the following three datasets which I separately fit to the Michaelis-Menten equation: $$ V= \frac{...
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1k views

Getting spline coefficients in R

I'm fitting a natural basis spline on a data set of the form: splineModel=lm(dist~bs(speed, df=3), data=cars) using bs ...
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Is it valid to solve an equation for multiple coefficients, then average them to obtain overall effect?

I have a regression model, the setup for which is as follows: I am using manyglm, a multivariate general linear model approach to determine the difference in several invertebrate species between two ...
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How do you interpret “explained” coefficients in Blinder-Oaxaca decomposition with considerable negative values?

For illustrative purposes, consider the example given on p. 473 of Jann (2008). However, instead of the difference and coefficients noted, let's assume the difference and coefficients were the ...
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Proving that $ (\hat{\beta} - \beta)' (X' X) (\hat{\beta} - \beta)$ is independent with SSE

Exercise: Prove that $ \mathbf{(\hat{\beta} - \beta)' (X' X) (\hat{\beta} - \beta)}$ and SSE are independent for a Least Squares Regression Model. Attempt: Note that by $'$ I denote the transpose ...
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Validity of Comparison of regression coefficient over time

Recently came across a study which related weight loss (DV) with number of IVs using OLS and suggested some IV might have decreasing effect over time. Sample of 50 patient, who were given different ...
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53 views

How to compare coefficients of multivariate multiple regression models, possibly using SUR

I am trying to compare the model parameters among three multivariate multiple regressions. All three models incorporate date from the same 97 individuals and share the same 4 independent variables (...
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125 views

How do you test persistence in an AR(p) regression?

An AR(p) process is defined as the regression of a variable against its p lags- $Y_t=c+\sum_{i=1}^p\phi_iY_{t-i}+\epsilon_t$. Persistence in an AR process can be defined as a measure of how much the ...
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Interpretation of Multivariate Adaptive Regression Splines (MARS) with Multiple Predictors

When it comes to multiple predictors, I've seen conflicting interpretations of MARS models and hoping for some clarification. Some fake results, let's say it's predicting household income via years ...
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777 views

Bootstrapping: resampling cases vs resampling residuals

I have this relatively small dataset (41 observations, 5 independent and 1 dependent variable) and built a linear regression model with interaction terms. Now I want to put confidence intervals around ...
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Logit Transformation: Interpreting the Coefficients

I'm currently doing an empirical project in econometrics. I examine the effect of globalisation and some other control variables on poverty, doing OLS cross section given a sample of 74 countries (...
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Bootstrapping from population to test regression coefficient equality

I have a multiple regression (e.g. $y_i = \beta_1 x_{i1} + \beta_2 x_{i2} + \cdots + \beta_p x_{ip} + \varepsilon_i$), in which I want to demonstrate that $\beta_1 > \beta_2$. I have the full ...
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371 views

Reported Coefficients for Glmnet using Caret

I understand GLMnet standardizes the predictor variables by default before fitting the model. After fitting, the computed regression coefficients are then destandardized to allow reporting in their ...
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Low variation in the explanatory variable: scale of the predictor

As explained in this post - > There are low variations in the explanatory variables, low variation of your explanatory variable might affect your results. The way I used to find that intuitive was ...
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Ratios, differences, and link functions?

I recently learned that with Poisson regression, you can model rate difference by using an identity link function, or rate ratio by using a log link function. Does that work the same way with other ...
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glmnet returning lambda that gives all-zero coefficients as optimal lambda

Before I start, I have already looked at the answers for related questions: How to interpret all zero coefficients in the results of cv.glmnet? Why is cv.glmnet giving a lambda.min that is ...
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259 views

What is the 'observed value' when we are talking about the error term

I understand that the error term is supposed to be the difference between the value produced by the population regression model / function and the actual observed value, but what is this 'actual ...
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143 views

Are regression estimates still reliable despite heteroscedasticity and non-normality

I am performing a simple linear regression with the lm() function to make statements about the association between the two variables. But I am not sure if my ...
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189 views

Combining Estimates from Conditional Quantile Regression : Meta-analysis?

Suppose i have several studies (e.g 5) and i use conditional quantile regression (e.g using the package quantreg in R) to obtain conditional quantile estimates at ...
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973 views

Fama-Macbeth cross-sectional regression interpretation

I have applied Fama-Macbeth cross-sectional regression on Fama and French five-factor model (2014). On the left-hand side are the portfolio returns for sixteen size - B/M portfolios. On the right-hand-...
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37 views

How do I generate appropriate group-level coefficients and standard errors for my regression?

I ran a mixed logistic model testing the influence of group (two-level) on a binary outcome, and I want to report the group estimates and their SEs in graph. However, I can think of two ways of doing ...
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334 views

Interpreting results from lasso regression?

I have a time series data set with about 2million observations and 31 variables, which I break to a few thousand using threshold value for my dependent variable. I am using lasso regression in R to ...
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362 views

Using repeated measures change/trend as a predictor variable

I have repeated measures of happiness for a sample of participants, and a single measure of satisfaction for each of the ...
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144 views

The effect of Measurement error on a Beta Coefficient

I am trying to show the bias of the slope coefficient that occurs when there is measurement error in the regressor. $$ Y = a + B* x_{i} + e_{i} $$ To find the beta coefficient, we can use the ...
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97 views

If all components of a hierarchical model have not converged, can we say that any parameters have truly converged?

I'm working with a hierarchical regression model of the following form similar to that presented in Peter D. Hoff's book, A First Course in Bayesian Statistical Methods: $\boldsymbol{Y}_j \sim \text{...
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A question on Multinomial Regression

Assume an experiment with 6 outcomes, dubbed A, B, C, D and E. For outcome A, there are Na subject, for B there are Nb subject and so on. Now assume we fit a multinomial regression using a Bayesian ...
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Violation of 1) normality of error terms, 2) heteroscedasticity and 3) spatially correlated error terms.Alternatives?

I am using linear (Ordinary Least Squares) regression to estimate the coefficients and model fitness for vegetation in an ecological study. However, after model fit, tests showed that the linear ...
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124 views

Angles expressed in degrees of arc as regression variables

I have binary count data as a response variable in my logistic regression. The independent variables include, among others, two variables of inclination and orientation measurements, annotated in ...