Questions tagged [multivariate-regression]

Regression with more than one response (dependent) variable.

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How do we know adding an uncorrelated variable to a regression will not change existing coefficients?

Say I have a regression with 3 independent variables and I decide to introduce a 4th variable and rerun the regression. A previous post states that the coefficient on an original variable will change ...
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13 views

Running a multivariate multiple regression with different numbers of observations of the outcomes

Say I have two dependent variables, y1 and y2, and two predictors, x1 and x2. I want to test whether y1 is affected by x1, and whether y2 is affected by x1 or x2. I have less observations of y2 and x2 ...
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22 views

Is single-output regression the same as univariate?

Similarly, is multi-output regression the same as multivariate regression?
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16 views

Whither multivariate regression?

I've been handed someone else's data (again). It's measurements of six proteins' levels from 20 human brain samples, 5 each of different stages of a disorder. I'd like to run a multivariate regression,...
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28 views

What to do with statistically insignificant dummy/categorical variables? [duplicate]

From the research I've done the common answer is that you can not remove insignificant dummy variables from a regression. I'm having a hard time finding academic papers or books that back up this ...
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1answer
52 views

Correlation in the residuals of a multivariate linear regression

I'm using a multivariate multiple linear regression model to predict 4 scalars out of multiple regressors. I'm not sure if this model is a good one and now I'm trying to asses the validity of the ...
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52 views

Multivariate zero_one_inflated_beta regression

I want to run a zero_one_inflated_beta regression with brms on the following multivariate formula: ...
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20 views

Regression when each observation of the dependent variable is a vector [duplicate]

The OLS formation $Y = \beta X$ and its derivation all have dependent variable $Y$ as a $n$ by $1$ vector, each entry of $Y$ is a scalar observation. But what if each observation is a vector of size $...
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18 views

when to give up in fitting a variable? [duplicate]

I would like to predict a variable from 5 features. I have bad scores (<50%) with all the algorithm I tried (Random Forest, Lasso, SGD, MLP). I would like to quantitatively assess if I should ...
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25 views

RStan v.s. simple lm for multivariate regression [closed]

I want to fit a multivariate linear regression, with Y1 ... Y4 as the response and X1 ... Xn as the explanatory variables. X1 and X2 are two components of a mixture, and X3 ... Xn environmental ...
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68 views

Mathematics behind single input, multiple output regression

I have sought some help and trained a regression model that takes in a single dependent variable Y and gives the three independent variable R, B and G as output. This has been done in attempt to ...
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22 views

Simultaneous equation model with endogenous regressors

Let's assume four dependent variables $Y_1$, $Y_2$ and $Y_3$ that are correlated. I want to evaluate the impact of several regressors: $X_1$, $X_2$ and $X_3$ on these 3 dependent variables using a ...
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27 views

How to get change of basis matrix for Canonical Correlation Analysis?

A bit of background: I am trying to create toy example of the Curds and Whey regression shrinkage algorithm in python. In a standard multivariate regression this algorithm uses canonical correlation ...
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39 views

Estimating conditional probability distribution from samples

I have three continuous variables, $X$, $Y_1$ and $Y_2$. All three are correlated. For a given value of $X$, the conditional probability distributions of $Y_1$ and $Y_2$ are typically bimodal. I'm ...
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49 views

Formulas for multivariate meta-regression

everyone! I'm digging in meta-regression and doing hand calculations using WLS to get better understanding of the topic. I'm fine with calculations for univariative model (that is, 1 covariate is ...
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1answer
28 views

How can I determine the overall Cox proportional hazard HR in multivariate analysis?

I am using the survival and survminer packages in R. I use the data and code below as an example. See also the output below. I ...
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2answers
387 views

Anyone know Multivariate OLS on Statsmodels? [closed]

I trying to run a mutivariate multiple regression using Statsmodels. Not sure if this is the best tool for this type of regression, so please do tell me if there's another package to which I should ...
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2answers
48 views

Regression with multiple dependent variables controlling for age and gender [closed]

I have multiple dependent variables (interval) and one independent variable (interval). I would also like to control for age (interval) and sex (categorical). Is this possible in SPSS? Moreover, my ...
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1answer
78 views

Adjustment for multiple comparison in bayesian multivariate regression model (using brms)

I am investigating age and timepoint effects on different (correlated) EEG parameters in a repeated measurements structure. I chose to use the brms R package to fit a bayesian multivariate model with ...
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19 views

Simulate multivariate outliers

Considering a multivariate linear model $\boldsymbol{Y = XB + E}$, where $\boldsymbol{Y, X, B}$ and $\boldsymbol{E}$ have dimension $n \times m$, $n \times p$, $p \times m$ and $n \times m$, ...
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18 views

Comparing the performance of multivariate with univariate linear regression model

Let $\boldsymbol{Y} = \boldsymbol{X\beta} + \boldsymbol{E}$ a multivariate linear model, where $Y \in \mathbb{R}^n \times \mathbb{R}^m$ a dependent variable, $\boldsymbol{X} \in \mathbb{R}^n \times \...
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23 views

Parameter estimation in bivariate linear models

I'd like to simulate data from a bivariate normal distribution to a regression problem. In other words, let $X = (X_1, X_2)$, where $X_1$ and $X_2$ be two matrices $n \times 1$. $X_1\sim N(3, 2)$ and $...
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53 views

calculating log likelihood for multivariate linear regression using R

I want to calculate a loglikelihood for multivariate linear regression. I’ve been calculated the log likelihood using multiple linear regression. ...
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37 views

Variance-covariance matrix of multivariate response, with censored values: MCMCglmm alternatives?

I have a dataset I need to analyze in which I'm interested in the relationships among several variables, after accounting for covariates that may affect some of those variables. More specifically, I ...
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1answer
79 views

Linear regression with stochastic gradient descent p-values

Is there any way to get summary statistics (p-value specifically) for the results of a multivariate linear regression ($y = X\beta + \epsilon)$ using gradient descent? Most online library ...
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18 views

intervention analysis with multivariate regression

Does intervention analysis make sense when one has multiple external regressors? How would one know if say, a level shift, is caused by a combination of external regressors or by a change in a law ...
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16 views

multivariate multiple regression - predicting vectors with different lengths

Obviously, multivariate multiple regression is the method of modeling multiple responses, or dependent variables (aka a vector), with a single set of predictor variables. Which techniques can I use ...
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22 views

Multivariate sparse regression - selective predictors

What do I do to find predictors that are ONLY/mostly related to one of several continuous response variables ? E.g., if you have (continuous) outcomes y1,y2,y3 and predictors a,b,c,... and a is ...
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1answer
106 views

Binary logistic regression with two dependent variables

I have a continuous independent variable, X, and two binary dependent variables, Y and Z. I'm trying to run a binary logistic regression that models the correlation between Y and Z. X = age, while Y ...
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28 views

multivariate multiple regression with probabilities as the dependant variable

I have a problem that involves multiple dependant variables, where each dependant variable is a probability and for each observation the probabilities sum to 1.0. I also have a range of independent ...
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29 views

Estimating parameters of multivariate regression using the maximum likelihood method with a uniform distribution of residuals?

Representation of regression in a matrix form: $$Y = XA + E,$$ where: $X$ - independent variables, $Y$ - dependent variables (observations), $E$ - errors, which have a uniform distribution, $A$ - ...
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37 views

OLS regression with multiple dependent variables that are correlated with each other

Suppose I want to see the impact of an explanatory variable $X$ on two different dependent variables: $Y_1$ and $Y_2$. Suppose also that I find that $Y_1$ and $Y_2$ are correlated. Assuming that all ...
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2answers
163 views

Predict a vector of values with constraints? [duplicate]

I am aware of a variety of methods for simultaneously predicting multiple outcomes known sometimes as multivariate regression/analysis. However, my situation is a little more special. I am trying to ...
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47 views

What is the correct way to follow up a multivariate multiple regression?

I recently conducted a study in which I used a series of multiple linear regressions to predict different outcomes (y1-y6) using the same set of predictor variables (x1-x8). My hypotheses were that ...
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1answer
196 views

Multivariate (Multi-responce) for negative binomial (GLM) in R

I developed a multivariate linear regression using lm() function in R. However, I am having trouble coding a Multivariate model in R for glm(), especially for the negative binomial. Can anyone point ...
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1answer
42 views

Hypothesis testing: significance

i conducted a survey that aims to find out if Australians prefer Australian phones over Chinese phones. My hypothesis states: Australians prefer Australian phones over Chinese phones This was ...
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25 views

Question about the correlation between residual/error and regressors [duplicate]

In multivariate regression: Why can the sample correlation between the error term and a regressor be ≠ 0, but the sample correlation between the residual and a regressor has to be = 0?
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58 views

Write Lack-of-fit Sum of Squares in Quadratic Form

Let \begin{equation} SSLF = \sum_{i=1}^{m}n_{i}(\bar{y_{i}} - \hat{y_{i}})^{2} \end{equation} then \begin{equation} \sum_{i=1}^{m}n_{i}(\bar{y_{i}} - \hat{y_{i}})^{2} = n(\bar{\overrightarrow{y}} -...
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29 views

Integrated mixed model testing correlation and difference in correlation across factors

I'm currently performing the following analysis : Computing $r_j(Y_{ij}, X_{ij})$ for each design cell (factor with level 1 or 0 for each unit) Estimating effect of factor on $r(Y,X)$ with a linear ...
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1answer
26 views

Null hypothesis for individual coefficient's p-value in multivariate logistic regression

When calculating $p$-values for individual coefficient $a_i$ (for variable $X_i$) in a multivariate logistic regression, is the null hypothesis that all $a$'s are zero? that $a_i$ is zero and others ...
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42 views

Testing for Heteroscedasticity of Multivariate Multiple Regression [closed]

I want to test for heteroscedasticity on a regression model with multiple dependent variables using R. I want to see if the indenpendent variable has an effect on the variance of all of the dependent ...
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1answer
77 views

Linear regresson with four values as input and two values as output

I have the following problem for a personal project of mine: I am solving a system of two differential equations that has 4 changing parameters. The output are two vectors of numbers. Let's say I am ...
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1answer
147 views

Multivariate regression vs. multiple univariate regression models

This is a naive question, but I am a little confused over the term "multivariate" regression. And note this question does not (to my knowledge) pertain to "multiple" regression. When people use the ...
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31 views

multivariate linear regression without b_0 [duplicate]

I created a multivariate regression following the scheme $$y = \beta_0 + \sum^n_{i=1}\beta_i*x_i$$ and got an average deviation ofaround 5%. When I tried the regression without the $\beta_0$ I got a ...
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54 views

multi-response outcome: multivariate or univariate regression?

I have a dependent variable which represents participants' responses on 20 words, coded as 1 = correct , 0 = incorrect Question: I am keeping the regression as univariate for now (as far as dependent ...
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229 views

multivariate normal distribution with mean vector 0 and covariance matrix Σ

I am newby in statistics and I have huge data with "p" variables and "n" samples. My data is a two dimensional matrix with "n" columns (each column is a sample) and "p" rows (each row is a variable). ...
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1answer
67 views

$R^2$ and p-value for multivariate linear regression with confounders

I am working on a project where I am interested in the following variables: Dependent variables: $y_1,\, y_2,\, y_3,\, y_4,\, y_5$ (continuous) Independent variables: $x_1,\, x_2, \ldots,\, x_{18}$ ...
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1answer
92 views

Conjugate priors for dynamic model $x_{t+1}=Ax_{t}+\eta_t$

What conjugate priors do we have for the model(multivariate) $x_{t+1}=Ax_{t}+\eta_t$, where $\eta_t\overset{iid}\sim N(0,\Sigma)$? I was thinking of using $\tilde{x}=Diag[x_1,...,x_{n-1}]$, $\tilde{y}...
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1answer
128 views

Different method for parameter estimation auto.arima

I am trying to fit a multivariate time series with the auto.arima() function in R. Since my time series has seasonality I included Fourier approximation and used ...
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17 views

Distribution of maximum variance explained by 1 variable

Say I do principal component analysis on $n$ variables, and I sort the fractions of variance explained to find the largest. What is the probability distribution for this figure? For context I just ...