Questions tagged [regression]
Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.
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Time series regression with overlapping data
I am seeing a regression model which is regressing Year-on-Year stock index returns on lagged (12 months) Year-on-Year returns of the same stock index, credit spread (difference between monthly mean ...
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Asymptotic property of tuning parameter in penalized regression
I'm currently working on asymptotic properties of penalized regression. I've read a myriad of papers by now, but there is an essential issue that I cannot get my head around.
To keep things simple, I'...
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Logistic regression for classification: are there any analytical solutions for the out-of-sample accuracy?
I run a binary logistic regression, with a binary dependent variable and a continuous independent one.
Now I want to evaluate the out-of-sample performance of the classification algorithm so obtained. ...
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Interpreting regression coefficients based on Andrew Gelman's re-scaling method
I have two predictors in a binary logistic regression model: One binary and one continuous. My primary goal is to compare the coefficients of the two predictors within the same model.
I have come ...
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Is autocorrelation not worth addressing with small N?
Consider a simple regression context in which there is a small set of response values, $Y$, and corresponding dates, $X$. (For simplicity, we can assume the dates are equally spaced.) We would like ...
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Bootstrap Prediction Interval: which residuals to use and which method?
I ask this question referring to the post: Bootstrap prediction interval, where a step by step method for calculating the prediction interval for linear regression models is explained.
In the ...
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Generalized additive model: choosing between cubic and thin-plate splines
I am using the gam function (from the mgcv package) to model a continuous response (a soil nutrient) in relation to a continuous ...
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Pope effect on pizza - Regression with presence absence and similarity data as dependent variables
I'm trying to figure out the right way to set up a regression when the dependent variables are presence absence data (of pizzas), and the similarity between the present pizzas. Bear with the story:
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When using L2 regularization outside of linear regression, do the same MAP estimation assumptions hold?
Some context is shared below, and my question is bolded at the end.
MLE from observation noise
In the linear regression setting, we learn model weights $\mathbf{w}$ to make scalar predictions $\hat{y}...
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What techniques are there to measure goodness of fit of Deming (orthogonal) regression?
Questions:
Even if there is no "widely accepted" technique, is there a useful-and-above-average technique for estimating goodness of fit in orthogonal regressions?
What are the pros/cons of this ...
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T-test for regression coefficients obtained from Ridge, LASSO etc
In ordinary least squares, for example in an experimental design case, I obtain the regression coefficents by:
$ \hat B = {({X^t}{X})}^{-1}X^ty$
Then, my null hypothesis for each coefficent is:
$...
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Efficient nonparametric estimation of confidence intervals and p-values for nonlinear regression
I'm estimating parameters for a complex, "implicit" nonlinear model $f(\mathbf{x}, \boldsymbol{\theta})$. It's "implicit" in the sense that I don't have an explicit formula for $f$: its value is the ...
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How do sufficiency statistics help in the interpretation of regression results?
One of the results why canonical link functions are widely used in GLMs is the existence of sufficiency statistics for the regression parameters, which in turn allow for:
... minimal
sufficient ...
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Why would I use ratio estimation instead of regression estimation to estimate means?
I am taking a graduate course on survey data analysis. I was recently introduced to ratio estimation and regression estimation.
I understand that using ratio estimator may be easier if we are ...
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Errors-in-Variables model for logistic regression
Simple question: I am familiar (though don't have tons of experience) with errors-in-variables regression. From what I have seen, this mostly is used with continuous outcomes in a linear model.
A) Is ...
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Minimizer weighted linear regression
In a regression problem, with $y=X\theta+\epsilon$ and $X$ is an $n$ by $p$ matrix
the ‘weighted least squares estimate is the minimizer $\theta^{*}$ of $f(\theta)=\sum_{i=1}^{n}\omega_{i}(y_i-x_i^{'}\...
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Poisson regression for binary data
I've been trying to read up on Poisson regression models, and it looks like it is possible to estimate such a model with a binary outcome. This has come up before on this site here (and somewhat here ...
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Using Fieller's theorem to calculate the confidence interval of a ratio (paired measurements)
If you have two means (with their own confidence intervals) and want to represent them as a ratio, how do calculate the confidence interval for the ratio?
An answer that was given to me, mentions ...
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How did Auguste Bravais come up with the regression line?
I am new to statistics and linear regression and I came across the face that auguste bravais discovered regression line but didn't realize it.
Auguste Bravais (1811-1863), professor of astronomy and ...
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Fitting a Logistic Regression via Brier Score or Mean Squared Error
Is there a name for a logistic regression model that has been fit using the Brier score (or equivalently the mean-squared error) rather than the cross-entropy?
I realise this isn't maximum-likelihood, ...
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Priors as Controls : Bayesian Regression
I have a general question about Bayesian Regression Modeling and how a prior might be used as a means to control for (close to) simultaneous events. I often face a situation where I have a time series ...
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Regression with dependent data with low dependence
Suppose you have data that is grouped in one way or another and therefore the assumption of independence is suspect. But you look at the intraclass correlation (or autocorrelation) and it is very ...
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Multi-target Regression Neural Network: Trade Off
Suppose you have a number of input features, for example:
x1 - temperature
x2 - day of the week
x3 - quantity of rainfall
...
You are trying to predict a number of output targets - using neural ...
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Assumptions of correlation test vs regression slope test (significance testing)
If my understanding is correct, then
the test on a regression slope in a simple bivariate regression - i.e. the test of $\mathcal{H}_0$: $b = 0$ in $Y' = a + bX$
and
the test of a correlation, i.e. $...
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Fixed Effects vs Lagged DV vs. First Differences Regression
What are the differences between using unit fixed effects, unit fixed effects and time fixed effects, lagged DV, or first differences to analyze a time series with 4-5 time periods and 35-50 units per ...
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Generalization of cumulative probability models for ordinal Y
There are many models in existence for ordinal $Y$, for example the proportional odds ordinal logistic model, the continuation ratio model, and the cumulative probit model. The first and third of ...
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Dantzig Selector, LASSO, LAD LASSO
I am wondering about this. When is it best to use Dantzig Selector (the infinity normed error measure plus the L1 regularizer) , the LASSO (the mean square error measure plus the L1 regularizer), and ...
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What do the terms "nearly-optimal rate", "near-minimax rate", "minimax optimal rate" and "minimax rate" mean in the context of posterior consistency?
Definition: A sequence $\epsilon_n$ is a posterior contraction rate at the parameter $θ_0$ if $$\Pi_n(θ: d(θ, θ_0) ≥ M_n \epsilon_n| X^{(n)}) → 0$$ in $P^{(n)}_{θ_0}$-probability, for every $M_n → ∞$.
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How to subset alternatives in nested multinomial logistic regression?
I am trying to predict whether or not captains in a particular groundfish fishery choose to fish on any given day and what variables may influence that decision. Originally I had planned on using ...
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Posterior consistency for scale-mixture shrinkage priors in low dimension?
Consider the model [1]
$$y_n=X_n\beta_n+\epsilon_n$$
$$\beta_i|\sigma^2,v_i \sim \mathcal{N}(0,\sigma^2 v_i), i=1,\ldots,p$$
$$v_i \sim \beta^\prime(a,b)$$
$$\sigma^2 \sim \mathcal{IG}(c,d)$$
where $\...
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On the defense of "change from baseline" even in randomized trials - can anyone question points in this article?
Many times I read a strong criticism on the change-from-baseline (adjusted for baseline or not) both in randomized and non-randomized. Several people advised "don't even think of reporting the ...
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In Ordinary Least Square (OLS) estimation: is the slope actually an "Inverse-variance weighting" estimator?
I am suspecting the answer is yes, but I'd appreciate help in proving it (even though we know that the estimator is BLUE, so it should probably hold).
For context:
An Inverse-variance weighting is ...
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Identifying non-linearities in relationship between variables
Logistic regression is often used to identify the effect of $x$ on a binary variable $y$ after adjusting for potential confounders $x_1,...,x_n$. In the medical literature, I will sometimes encounter ...
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Minimizing MISE to find consistent estimator
Consider kernel regression estimation of the mean function $m$ of the process
$$y_t = m(x_t) + \epsilon_t,$$ where $\epsilon_t$' s are correlated with covariance function $R(s,t) = \exp \{-\lambda|s-...
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What is difference between interrupted time series and regression discontinuity design
Say that one has data over time, t, on an outcome, y. There is an event that happens at t==0....
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Robust Gamma Regression
I am modeling some spectroscopic data where the response of the instrument to the size of the input is strictly positive and non-linear. Gamma regression seems like a good choice to explain the data, ...
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Geometrical interpretation of L1 regression
I have found the following image (or a similar version) in a lot of books related to penalized linear models. I get the insight of this image. The ellipsoids are the solution of the linear regression ...
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Is there any geometric intuition on least absolute deviation regression?
There are a lot of geometric intuitions for regression with least square, e.g., projection, orthogonal, etc. (This and this answers are good examples.)
Is there similar geometric intuition for least ...
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Is lasso always outperformed by adaptive lasso?
I have been reading some papers and I understood that adaptive lasso has the Oracle properties which lasso lacks. Does that mean adaptive lasso always better than lasso (let's focus on the simple ...
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Linear model with hidden variable
I have come across a somewhat unusual (I think) estimation problem. I have two "coupled" linear regression models,
$$Y = a + b x + \epsilon, \quad Z = c + d x + \nu$$
where $Y,Z,\epsilon,\nu$ are ...
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Can I use bootstrap results at the observation level?
I have read quite a bit of bootstrapping, but the issue I want to address seem not to appear.
Consider a simple regression model:
$$ y_{i} = \beta_{0} + \beta_{1}x_{i} + e_{i}$$
I am aware that ...
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Assumptions for PCR and PLS
I am writing up a report on fitting Principal Component Regression (PCR) and Partial Least Squares (PLS) to my data-set.
A similar question: Model assumptions of partial least squares (PLS) ...
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Linear Regression - Confidence interval for mean response vs prediction interval
I understand the concept of a confidence interval for the mean response (fitted line) for simple linear regression $y$ = $\beta_{0}$+$\beta_{1}$$X_{i}$. It is that taken over many times, with 95% ...
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Interpretation of smoothing spline
This question is about interpreting the results from non-linear regression models, especially when using regression splines. The numerical output is not very informative when interpreting the effects, ...
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Can I calculate Cohen's $d$ from multiple regression coefficient?
Question: Is it appropriate to calculate Cohen's $d$ (effect size) from the regression coefficient of an independent categorical variable?
Background: My regression coefficient represents ...
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Testing for conditional independence: What's the correct way?
My goal is to check if two variables $X$ and $Y$ are conditionally independent given $Z$.
For simplicity, let's assume the joint distribution is multivariate normal. In this case, we can compute ...
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Rule of thumb for excluded variable in Heckman selection model?
I'm working on a project that involves the use of a Heckman selection model (more specifically a Roy or move-stay model, which is essentially a two-sided Heckman) of the following form:
$$ Y_{i1} = ...
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Bias Variance tradeoff from a Bayesian perspective
I know the general question about bias variance has been asked before. I understand the frequentist approach and the concept of model selection and the impact of bias and variance on "accuracy" of a ...
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R packages that work with biased samples
I'm working with a biased sample of web users. I'm only able to track responses of users who have navigated my site in a certain way, and I'd like to run an analysis to determine how certain factors (...
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Standardizing count variables in panel data with overdispersion - R or Stata
I'm running a regression where the dependent (response) variable is a highly dispersed (slightly zero-inflated) count and the explanatory (independent or predictor) variables are continuous, counts as ...
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