Tagged Questions

Refers to any model where the a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

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6
votes
2answers
220 views

Why is GLM different than an LM with transformed variable

As explained in this course handout (page 1), a linear model can be written in the form: $$ y = \beta_1 x_{1} + \cdots + \beta_p x_{2} + \varepsilon_i$$ , where $y$ is the response variable and ...
0
votes
0answers
8 views

selecting genes specific/agnostic to condition

I have a microarray transcriptomics experiment. The design of which is something like this : ...
0
votes
0answers
20 views

Given a covariance matrix from a Linear regression, how do I calculate the standard error of the coefficients?

I have an OLS with autocorrelation in the residuals. I'm using python statsmodels, and found that there is the sandwich_covariance matrix, which can cal Reference to Newey-West covariance matrix: ...
0
votes
1answer
48 views

Non-linear Model vs Linear Model for a dataset

I have a time series dataset for a city. The dataset contains rainfall amount and the number of repairman requests to a company. The company has 20 shops in different blocks of city and the rainfall ...
0
votes
0answers
21 views

Troubles reporting transformed variables for log and sqrt into a general equation

Good morning everybody, I see CrossValidated has really high level of questions and answer; I am just a student so I hope this question is not too basic... Suggestion of further readings available ...
1
vote
0answers
41 views

Linear model / models analysis

Above are three plots of the Linear model I am trying to analyze. The first one is a basic plot of the linear data: ...
1
vote
0answers
26 views

What is Linear Projection [closed]

Can anyone help explain the linear projection and its application? In Wooldgridge's textbook of Econometrics, he introduced the basics of linear project, which I understand what it is but I still ...
0
votes
1answer
29 views

Modelling interaction

How does adding interaction term in the model adjust for it or why do we need to add interaction? I am working on logistic regression model with treatment and race as predictors. I have added ...
12
votes
3answers
458 views

How to discuss a scatterplot with multiple emerging lines?

We have measured two variables, and the scatterplot seems to suggest multiple "linear" models. Is there a way to try to distill those models? Identifying other independent variables has turned out to ...
0
votes
0answers
23 views

How to improve linear model generalization when autocorrelation is present?

I have features $X_t$ and response $Y_t$ (all continuous variables) and my objective is to find the best estimate of $f(X_t)=Y_t$ where $f$ is linear, and 'best' is defined as lowest generalisation ...
1
vote
1answer
35 views

LSmeans - Unbalanced data with interactions

I wish to analyze an unbalanced data set with 3 variables Tleaf, Tair, and orientation (factor with two levels). Considering the effect of the factor "orientation", I wish to determine if "Tair" has a ...
1
vote
1answer
42 views

What is the benefit of knowing the F statistic in multiple linear regression?

One of the basic figures you get when running multiple linear regression using almost any off-the-shelf software is the F statistics. However, I cannot recall one situation, where the F value was low ...
2
votes
1answer
153 views

Is a linear model OK?

I carried out a linguistics experiment where I gave a text for people to comment on. I recorded and transcribed their comments. I would like use the number of utterances per sentence in the text they ...
2
votes
0answers
53 views

Show alias coefficient of Plackett Burman design equals $r_{ij}=\frac{c_{1i}'c_{2j}}{N}$

Consider a Plackett Burman design with N rows and let $\beta_{1}$ be the of the regression coefficients corresponding to the main effects and let $\beta_{2}$ be the vector of the regression coefficients ...
0
votes
0answers
23 views

Drop1() and Summary() on lm object

I need to analyse unbalanced data through linear regression: modJuin=lm(TleafMax~TairMax*orientation, na.action="na.exclude", data=aJuin) "TairMax" is a ...
0
votes
0answers
29 views

How to compute/run LDA with 3 classes

I couldn't find one example on how to compute LDA with 3 classes (nor what is the algorithm). for example i have the following observations and classes: (each observation in one-dimensional) $ ...
1
vote
0answers
30 views

Identifiability in linear regression and time series

The multivariate linear regression model is given by $\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}$, where $\boldsymbol{\epsilon} \sim \mathcal{N}(\mathbf{0, ...
3
votes
1answer
102 views

How can I optimize coefficients of an arbitrary model?

This might be terribly easy but I'm probably lacking the keywords to search for. Assume the following (dummy) data: ...
2
votes
1answer
43 views

Multiple Linear Regression: Obtaining a Stable Model

I am working with a data set of ~1200 rows and 60 variables, and I'm trying to build a multiple linear regression model. I do this by separating 10% of the dataset to be used for validation and I use ...
0
votes
0answers
28 views

Fuzzy regression (using linear programming)

I want to replicate a fuzzy regression using a linear programming problem approach. I have the following information: " A fuzzy regression analysis with only one independent variable X results in ...
5
votes
1answer
112 views

Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom

Background Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$ where $\mathbf{\beta}$ ...
1
vote
1answer
50 views

Comparing coefficients of linear “ Stochastic Frontier Production and Cost Functions” in R

I am using the function frontier::sfa() in R to obtain the Stochastic Frontier Production and Cost Function as followed: ...
0
votes
0answers
21 views

Linear model with longitudinal data, predicting difference

I have a set of data for 2 visits in patients and I would like to see whether there is a effect of a difference of one variable on another. So, lets say, my variables are A, B, age + gender. I want ...
1
vote
0answers
17 views

Multiple objective allocation function

I have an allocation problem where, for a given good, I have buyer $i$ willing to buy up to quantity $b_{s,i}$ and seller $j$ willing to sell up to quantity $s_{s,i}$. There are $N$ buyers and $M$ ...
1
vote
0answers
13 views

Why normalized feature weights for linear regression are bad feature importance predictors

I am trying to interpret a linear regression model. I assumed using absolute value of feature weight coefficients as indicators of influence of input variable onto output variable. However, it seems ...
0
votes
0answers
13 views

Probability that independent variables have significant regression coefficient

suppose to have a dataset $X\in \mathbb{R}^{n\times p}$ and $y\in \mathbb{R}^n$. Independent variables. In general $cor(X,y)\neq 0 $ and so if we fit a linear model we can have that some of the ...
0
votes
1answer
23 views

Refitting with different contrasts vs. pairwise comparisons

Say, I fit a linear or generalised linear model in R with dummy coding (contr.treatment for ...
2
votes
1answer
46 views

Ok to use 0 and 1 for a varaible in a linear regression?

Ok this is a simple quesion that's been bugging me. The question is how to encode a linear model variable with only two possible values and avoid any trouble introduced by using zero. Say you have a ...
0
votes
0answers
34 views

Estimate the covariance matrix of a normal distribution if the mean vectors is given by a linear rule

Let $X=(x_1,\ldots,x_n)^\top\in\Bbb{R}^n$ be a random vector that follows a multivariate Gaussian distribution with known mean vector $\mu=(\mu_1,\ldots,\mu_n)^\top\in\Bbb{R}^n$. The covariance matrix ...
1
vote
0answers
25 views

Performing a linear regression on small dataset and trouble with modeling small predictor values

I have a dataset. y: the dependent variable (representing a ratio between the number of objects bought with the given money & the total number of objects bought) x: the independent variable ...
2
votes
1answer
88 views

Interpreting intercept for the log model in linear regression in R for small predictor

I have a dataset. Assume that y is the dependent variable and x is the independent variable. My goals for this analysis is mainly on the following hypothesis: Expecting x=0 to imply y=0 Expecting ...
3
votes
3answers
61 views

Simulation from linear model with additional variables

I want to test the performance of a variable selection method in linear regression with normal errors using simulated data: $${\bf y}= {\bf X}{\bf \beta} + \epsilon,$$ where, as usual, ${\bf y}$ is ...
0
votes
2answers
32 views

Proving Linear Estimator (beta) is BLUE?

In the book Statistical Inference pg 570 of pdf, There's a derivation on how a linear estimator can be proven to be BLUE. I got all the way up to 11.3.18 and then the next part stuck me. After ...
0
votes
1answer
40 views

adjustment of covariates in linear model

I am trying to understand the adjustment of covariates in the linear model such as multiple logistic regression. How does adding a covariate adjusts the coefficients for that covariate (any intuitive ...
0
votes
1answer
57 views

Compare linear regression models (same and different response variable)

How can I (1) compare two linear models between years and (2) Can I compare 2 models with different response variables? My data have 4 variables: y_meas, x, year, y_calc. "y_meas" is a lab measured ...
0
votes
0answers
23 views

Building a linear mixed effects model?

Study Design I have a dependent variable (PP), collected under two different conditions (Condition) in ten subjects (Subject) of varying heights (Height), across three different trials (Trial). Both ...
1
vote
3answers
42 views

Compare influence of same set of independet variables on two different dependet variables

I'm currently doing two multiple linear regressions. Each of them with the same set of predictors (measurements for real estate quality) $X_1,...,X_n$, but with different dependent variables (one of ...
2
votes
1answer
45 views

Random intercepts as response variables: Is there a name for this method?

I'm trying to find the name of this method (and ultimately a reference). The approach is as follows: 1) Fit a mixed-effect model with a random intercept $$ E(Y_{ij})= ...
0
votes
0answers
55 views

How to calculate p value from ANOVA function for LMM results?

I have used ANOVA function so that I can get the overall p value of significant factors: ...
0
votes
0answers
28 views

To get the overall significant p value, am I on the right track for LMM?

According to this document: http://www.bodowinter.com/tutorial/bw_LME_tutorial2.pdf I can get the overall p-value of fix effects by comparing models that I would like to know to null model. In my ...
0
votes
0answers
15 views

Temporal trends with missing values

I need to calculate the temporal trends for some climate variables with missing values. For example, last frost days defines as the last day of year with minimum temperature less than 0C. However, ...
0
votes
0answers
18 views

Can I combine two pairwise comparisons?

I am using LMM in lmer. To find the most optimal model, I compare models of three-level with two level using ANOVA function. If it turns out that no significant difference between these two, then I ...
3
votes
1answer
79 views

Design of matrix of contrasts in R

I am doing some post-hoc comparisons (in lme4, but here I'll just present a simple linear model), and I am having a hard time making sure that I am building the right matrix of contrasts to test ...
0
votes
0answers
30 views

Hidden Markov Models relationship

I have a question regarding a small investigation that I have been conducting into the relationship between the length of observation sequence, T, on which two decoders (BCJR and classic Viterbi) ...
0
votes
0answers
6 views

example of a non-trivial data where leverages would all be equal

i was asked to describe a non-trivial data (n not equal to =/1) example where the leverages would all be equal for QR decomposition question. could someone help?
2
votes
1answer
58 views

Consistency of OLS in presence of deterministic trend

For consistency of OLS estimator for linear model $$ y_i = \beta^T x_i + \epsilon_i, \; i = 1,\cdots, n, $$ the model assumptions are usually (the ones I am familiar with) The sequence of random ...
0
votes
1answer
76 views

Linear model- Understanding performances on training and test sets

I have a small normalized data set, 30 observations and 18 Predictors. All are continuous and some variable are related. I ran linear regression on it using Weka. The model automatically dropped some ...
3
votes
1answer
171 views

Rule of thumb to rule out reverse causality in the OLS model

Let' say I have a regression model: $y=a+b*x+error$ Suppose $x$ is income and $y$ is consumption. The hypothesis is that higher income leads to higher consumption and hence, the coefficient on $x$ ...
2
votes
2answers
42 views

AR terms and independent variable as regressors

After trying several models with my data, R^2 and p values are showing my model looks like below. ACF plot tells me AR term is significant. Insights into data tells me change in 'x' would have ...
2
votes
0answers
214 views

Mixed effect linear regression model output interpretation

I just fitted the following linear mixed effects model: ...