Questions tagged [multivariate-regression]
Regression with more than one response (dependent) variable.
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A joint model about 6 years agricultural crop research data
I encountered a difficult statistical problem in the process of analyzing my agricultural crop research data. I would like to ask for your comments and suggestions.
This research has been carried out ...
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24 views
MSPE predictor of MA model
Assume $e_i=(\epsilon_i+\epsilon_{i+1})/2, i=1,...,n$ where $\epsilon_1,...,\epsilon_{n+1}$ are iid with mean zero and variance $\sigma^2$. Then $e_i$ are the moving average errors. Now, consider the ...
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Interpretation of the coefficients from quantile regression with dummy independent variables only
I have a data set with only categorical variables, some are nominal and some are ordinal, but I assume there will be non-linear relationship between output and order of ordinal variables, so I have ...
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15 views
Bayesian multivariate regression
I am trying to solve the below multivariate regression problem by building a fully Bayesian model-
\begin{align*}
\mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{E}
\end{align*}
where $\mathbf{Y} \in R^{n\...
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17 views
Multiple dependent variable model, What model to use?
I need to develop a model to predict the best budget allocation scheme for x budget between n posibilities (products or product types) for a certain person. Aside from the budget, there are multiple ...
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1answer
17 views
How does AMOS or other SEM/path analysis software estimate missing data?
I'm currently writing a paper as a hopeful publication. I'm using AMOS to run path models. But I think my question can apply when utilizing other path analytical software.
I have one path model that ...
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9 views
Optimizing Frobenius norm in R
Suppose that $Y \in \mathbb{R}^{n \times p}$, $X \in \mathbb{R}^{n \times d}$. Is there a function in R that gives the optimal solution $\hat{B} \in \mathbb{R}^{d \times p}$, which minimizes $\Vert Y-...
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20 views
How to perform multivariate multiple regression using quantitative variables in R
I would like to try multivariate multiple regression with 5 dependent variables, 3-4 independent variables. All are continuous quantitative variables and are standardized data (because some of them ...
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1answer
17 views
Scaling explanatory variable by constant in multivariate linear regression
Suppose I have a model with $n$ observations $$Y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \varepsilon_i$$ and suppose that I obtained estimates $\hat Y$, $\hat \beta_1$, and $\hat \beta_2$ from ...
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2answers
28 views
consistent estimation of quantiles (without overlapping quantiles)
I would like to forecast quantile ranges. The observations are assumed to be heteroscedastic. Mostly, I am confronted with the problem that quantile regression results for different quantiles do ...
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12 views
MANOVA or difference scores?
I have a research design where participants are asked how much they want to donate to two different children in need. The goal is to measure whether they will be equitable (give equally to both ...
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1answer
16 views
Forecasting the daily visits when I have the data for other stores
I have the number of people visiting stores for each day, but sometimes one or several store do not send data for a particular day. How can I leverage the data I have for the stores that sent me data ...
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1answer
26 views
How to deal with different lengths of dependent variables for Multiple Multivariate regression?
So this question is probably part statistics and part r studio related. I want to run a Multiple Multivariate Regression with 13 dependent variables and 4 predictors. The 13 variables are scales from ...
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27 views
Proving residual/$\sigma \sim$ $N(0,1)$
I would like to proof that
$$\frac{Y_i - \hat Y_i}{\sigma} \sim N(0,1)$$
holds where I refere to the general multivariate regression case, i.e. $Y_i = x_i \beta + \epsilon_i$ with $\epsilon_i \sim N(0,...
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19 views
Why would a multivariate regression of two correlated output variables be worse than assuming independence?
I have 7 features and 2 outputs. The outputs are definitely highly correlated (wingspan and standing reach, which are two common measurements for basketball players). I have created two models using ...
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1answer
43 views
How to identify latent factors on only one observed variable
Is there an approach to identify latent factors impacting the outcome of only one observed variable?
I have a number of observations for one variable and assume that it is affected by two latent ...
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6 views
How to assign relation between categorical input and any given variables for Multivariate regression models with a backwards method in R?
I am kind of beginner level in R and I do apologize for any misunderstanding and typo-error. I am trying to perform a statistical analysis for a measurement, which is a function of time. I was told by ...
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25 views
Intuition for Hotelling's T^2 Test
I have been learning about Hotelling's $T^2$ test from Multivariate Statistics: Old School. The test is given by $T^2 = \nu\cdot\text{trace}(\bf{W}^{-1}\bf{B})$. The author shows that in the case of ...
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When building a linear regression model using PC1 from a PCA, does it matter that some of the variables explaining PC1 are collinear?
Let's say for instance, I measured a biological variable at different sites. I also measure a bunch of environmental variables, and I create a principal component analysis using those environmental ...
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23 views
Fitting a multivariate linear regression with different residual variance for each outcome (using a mixed effects model in R)
In a small simulation, I am fitting a multivariate normal model to predict two outcomes Y1 and Y2, while also modelling the covariance between them. This can be done through a mixed effects model (...
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63 views
Multivariate quantile regression group lasso in R
I'm trying to fit a multivariate sparse quantile regression model with group lasso. The regression is multivariate as there are several dependent variables, $Y=(y_1,\dots,y_k)$. The selected $X$s must ...
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13 views
Multivariate Regression with Unknown Number of Responses
I would like to perform a regression task in which the number of response variables differ for each observation. As a simple example, this could be taking a greyscale picture and aiming to determine a ...
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1answer
48 views
Testing equality of quantile regression slopes at different quantiles
How do I test if the quantile regression slopes are equal for different quantiles?
E.g. I run a quantile regression at 5% quantile, 50% quantile (median) and 95% quantile and obtain the slope ...
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33 views
Multivariate Multiple Regressions
I have 24 multiple regression equations (24 dependent series and 24 independent series) and want the coefficients to be equal.
How do I combine them?
I allow for correlation of errors and tried SUR, ...
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16 views
Does multivariate multiple regression take into account correlated outcomes? [duplicate]
Thank you so much for your time. I am running an analysis where I explore the association of the same predictors across multiple outcomes (these outcomes are correlated). My understanding is that when ...
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31 views
Investigate correlations in dependent variables: interpreting EFA
Background
I have a dataset that includes 5 dependent variables (different genes expression levels, all continuous) and independent variables (a categorical variable -treatment-, a few covariates and ...
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14 views
Is multivariate linear regression appropriate with a fully repeated measures design
I am trying to set up a multivariate linear regression model but am having difficulty figuring out as to whether it is appropriate for my dataset.
For a group of participants, I have 3 response ...
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231 views
Autoencoders For Multivariate Time-series Anomaly Detection
I have a multivariate time series of size (1e6, 15) and would like to fit a LSTM autoencoder. I prepare data with multivariate rolling windows (one step rolling) where each sample has (1, 5, 15) ...
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21 views
Multivariate Regression Tree
I need to build a Multivariate Regression Tree.
Looking at Scikit-learn's Multi-output Decision Tree Regressor it seems that what they do is define as many regressor as there are dependant variables. ...
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32 views
R-squared fot multivariate regression
I have an output of recalibrated VARX model, which means for each 500 points of my data set I have trained a model and predicted the next month values using that ...
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0answers
49 views
D-optimal design with nuisance parameters
I am a mechanical engineer trying to develope an optimal design of experiments in a problem with nuisance parameters. I would like to calculate the parameters $\mathbf{d}$ to optimally estimate ...
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113 views
Hyperparameter Tuning with Keras / Tensorflow for multivariate time series regression
The model
I am training a dense feed-forward NN using the Keras API on Tensorflow.
Each sample of the training set defines $\mathbf{X_t}$ and $\mathbf{Y_t}$ of an observed time period $t\in T$. Input ...
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Sas linear regression deciding on subgroups
I want to model the Total Volume as a function of the two variables Units and Price.
I want to find out whether to model the total volume on the category as a whole or whether to model total volume by ...
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Formula for estimates of multivariate linear regression
Does anyone have links to a source which gives the mathematics behind how coefficients, standard error's and covariance structures are estimated in multivariate linear regression?
There are plenty of ...
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9 views
What type of statistical test should I perform?
What statistical technique would I need to carry out if I want to see if there is a significant differences in the number of units purchased when classifying observations based the variables Age, ...
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31 views
Confidence Intervals for the coefficients of a Multiple Multivariate Regression
I have a functional response [ y(t) ] that I have discretized on a grid of q points, and 3 scalar regressors (x1,x2,x3). I have replaced the response function with an nxq matrix Y and this lead me to ...
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11 views
Determine the proper level of heteroskedasticity
My dependent variable is house prices and I need to understand whether the level of heteroskedasticity in this plot of residuals vs fitted values is low enough to accept the existing multi-variate ...
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Regress 4 values based on an input matrix with shape of (16,5)
Problem: I need to regress 4 values (which quantify how much a user likes a specific topic). I am performing simulations, so I know the ground truth (the real 4 values of the preferences)
Input Data ...
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31 views
How to model a system of equations as a standard linear regression problem
Having a sample of two independent and two dependent variables (), and considering that and , and knowing that , how can I model this problem as a standard linear regression problem?
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How to approach modeling multiple outcomes with differing distributions in Bayesian setting?
I'm planning a replication study, and am exploring various ways of analyzing the data. In a single study, I will have two outcome measures, which are expressed on completely different scales - one is ...
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1answer
26 views
Appropriate model that considers both treatment and risk factors for outcome
Consider a retrospective study to be planned with
200 patients with
5 risk factors (such as age, disease score = disease severity, hypertension etc.) which may affect
(a) outcome as such (older ...
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0answers
22 views
Multivariate Regression: Both Continuous and Categorical Predictor Variables
I am involved in a meta-analysis assessing the role of multiple baseline characteristics (e.g. age, BMI, symptoms and signs) in a given disease.
One element of our analysis includes a multivariate ...
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In multivariate regression, under what condtions is $var(X_i\epsilon_i')$ positive definite?
Suppose we have $(Y_i, X_i)$, with $Y_i$ an r.v. in $\mathbb{R}^k$ and $X_i$ an r.v. in $\mathbb{R}^p$ and suppose the covariance matrix of $X_i$, $E(XX')$ is positive definite. Now we can estimate ...
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Exclusion of Spuriousness With More Dimensions?
The usual way of excluding spuriousness in multivariate correlation is to increase the number of samples. However, if increasing the dimensions of measurements produces an unusual magnitude of ...
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1answer
354 views
What is MCRMSE (mean columnwise root mean squared error)?
The MCRMSE evaluation metric was used in the Kaggle Competitions Africa Soil Property Prediction Challenge(6 years ago) and
OpenVaccine: COVID-19 mRNA Vaccine Degradation Prediction(On-going) ...
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1answer
46 views
Are the outcome and predictor variables in a logistic/linear regression interchangeable?
Consider the following example. I am studying the mutation burden across three subtypes of cancer. In my dataset, I have individuals without cancer (controls) and individuals with cancer (cases); the ...
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Wald test / seemingly unrelated regression on models with clustered standard errors in R
I am trying to conduct a Wald test (aka seemingly unrelated regression) on multivariate models with clustered standard errors in R. This is easy to do in Stata, but I cannot figure out how to do it in ...
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2answers
78 views
Multivariate regression (multi-target regression) dataset where some regression coefficients are known to be zero
I'm looking for a sample dataset for multivariate linear regression - also known as multi-target or multi-output. Preferably with more than 10 inputs and more than 10 outputs. There don't seem to ...
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42 views
How to predict unknown time series in using Facebook Prophet?
The problem is predicting hits on different stories published on a website. I am aware that for this kind of time series forecasting, facebook prophet is a popular library. However, it seems in ...
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0answers
34 views
SEs in multivariate regression
To avoid confusion, my question refers to multivariate regression as multiple dependent variables for the same set of independent variables.
As far as I understand (see e.g., this question), the ...
