# Tagged Questions

This tag is a signal that the question focuses on a problem particular to multivariate analysis, such as multiple correlations or interactions.

93 views

### Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
47 views

### Getting the prediction standard error from a natural spline fit

I'm fitting a natural spline fit to some data points. I'd like to estimate the prediction error for the predicted value. In linear regression (I agree that natural spline is also a linear regression ...
87 views

### How do you check the linearity of a multiple regression

With Univariate regression it's very easy to see if the correlation is linear or otherwise, but in a multiple regression things can look very complicated, polynomial or other correlations can be ...
356 views

### Fitting a zero-inflated negative binomial regression with R

In this thread, I laid out a problem involving fitting a model that attempts to use minor league baseball statistics to predict success at the major league level (explained in full in the thread). ...
209 views

### Why is correlation between y and $\hat{y}$ in a model with and without intercept equal?

I consider a very simple example with two models like this; ...
111 views

### Relationship between LASSO T and LARS number of steps k

We can see on the figure (cf Least Angle Regression p30, Efron, Hastie, Johnstone, Tibshirani - link: Least Angle Regression) that there is a direct relationship between: LASSO T absolute norm of ...
66 views

### Regressing on many outcomes in a spatial model

I'm measuring many microbe populations in a 'river model' ecosystem by sampling at two points. I want to test the hypothesis that key species upstream are the best predictors for any given population ...
141 views

### Variable Selection One by One vs Simultaneously

The high dimensional variable selection problem is really popular now. But I have a question: If I do simple linear regression regressing one response variable on 1 covariate at a time first and then ...
497 views

### Multivariate normal distribution of regression coefficient?

While reading a textbook on regression I encountered the following paragraph: " The least squares estimate of a vector of linear regression coefficients ($\beta$) is  \hat{\beta} = ...
48 views

### Should I de-mean a predictor variable before a dummy interaction

Suppose I have the following time-series linear model where $\beta$ is misspecified: $Y(t+1) = \alpha + \beta X(t) + \sum_{i=1}^{10000}\gamma_i Z_i(T) + \varepsilon$ where all parameters are in ...
71 views

### Variance partitioning - why be cautious?

I'm about to use variance partitioning to interpret my results of a given model and across models and have come across various criticisms of it most notably by Pedhazur (1982, 1997). Also, the ...
50 views

### Finding the experimental region of a linear model

Given a set of data with many independent variables and a single dependent variable how can I find the "experimental region" of the resulting model? This is the region within which we can make valid ...
94 views

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### Assumption violations with heteroscedastic data and OLS regression

I'm trying to model the typical performance of an experimental approach I've developed. I have a total of 3000 observations for 72 different case studies. My observations consist of a reading for ...
42 views

### May I validate a model after shrinkage?

I am doing a logistic regression using Frank Harrell's rms package. I went through the steps shown in his book and the rms ...
52 views

### Calculate goodness-of-fit (with deviance) to compare averaged models?

I need to compare the goodness of fit of several averaged logistic regression models by calculating the deviance explained. I'm using the MuMIn package in R to ...
93 views

### Selection of regressors

I have a question about the package leaps which I am using for model selection. I would like to compare 4 different selection methods: forward, backward, stepwise and best subset. I used the code ...
55 views

### Relationship between estimates in 2 linear models

I am considering two linear models with model matrices related as follows: \begin{equation*} \text{Model} \ 1 \\ \begin{bmatrix} \mu_1 \\ \mu_2 \\ \vdots \\ \mu_n \end{bmatrix} = \begin{bmatrix} 1 ...
76 views

### 95% CI or standard error of predicted risk in Cox regression using R

I am doing a multivariate Cox regression. I got the predicted risk for a new scenario based on the existing Cox model in R using function predictSurvProb in the ...
748 views

### can ordinal variables be used as predictor for linear multiple regression analysis?

Part of my thesis tries to investigate the extent to which students "test Score" on the topic of electrical circuits in physic can be predicted from how they find the topic to be "interesting" ,Their ...
76 views

### Can we find bounds on R-squared?

We know that as the number of independent variables increases, the coefficient of determination $R^2$ will increase but the adjusted $R^2$ may or may not increase. In the following question for the ...
108 views

### Variable selection with restricted cubic splines

Is there any function in R for doing variable selection (backward elimination) in a multiple logistic regression using restricted cubic splines like mvrs procedure for STATA?
82 views

### Principal component regression and including variables not in the PCA

I performed a PCA on some data related to habitat (different types of vegetation cover, soil water etc.), but there were some variables that I did not include in the PCA because they were not strongly ...
284 views

### When using glmnet how to report p-value significance to claim significance of predictors?

I have a large set of predictors (more than 43,000) for predicting a dependent variable which can take 2 values (0 or 1). The number of observations is more than 45,000. Most of the predictors are ...
158 views

### Simulation of multivariate correlated variables

I am trying to recreate the simulation method used in the paper Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression by Vittinghoff and McCulloch. The setup is the following: We ...
115 views

### Literature on robustness of regression assumptions

In my OLS regression not all assumptions are perfectly met, but I read that due to a large sample size there is a certain robustness to assumptions (my sample is 2500 people). E.g. the DV isn't ...
391 views

### Calculating standard errors for contrasts of parameter estimates of a (multiple) linear regression

I am running regression analyses in matlab with glmfit and calculate significance of contrasts of parameter estimates by using standard errors. Somehow however, the results I get are not consistent ...
541 views

### Differences between Stata & SPSS in multiple regression outcomes

I'm a graduate student working on a thesis whose aim is to test complementarity between 2 practices (CI and INNO, according to theory of supermodularity). To do so, I calculated two new variables ...
118 views

### Independent categorical variables and multiple regression with numeric dependent variables

Firstly I am very very new to stats... I am trying to find a relationship between a dependent numeric factor and have 6 nominal, 1 ordinal and 4 numeric independents. I have been using the category ...
29 views

### Estimated Treatment Effect in the full sample is not between the estimates of the stratified samples?

I am estimating the relationship between students' math scores and using a supplemental math software. I've adjusted for some demographic variables in the model. In my first model, I use the full ...