Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [linearity]

63 questions
18
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2 answers

The linearity of variance

I think the following two formulas are true: $$ \mathrm{Var}(aX)=a^2 \mathrm{Var}(X) $$ while a is a constant number $$ \mathrm{Var}(X + Y)=\mathrm{Var}(X)+\mathrm{Var}(Y) $$ if $X$, $Y$ are independent However, I am not sure what is wrong with the…
lanselibai
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16
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1 answer

An Unexpected Expectation!

Due to the linearity property of the expectations, we can write $E(X+Y) = E(X)+E(Y)$. But in Chapter 6.1 of the book, "Counterexamples in probability", the writer, Jordan Stoyanov argued that this is not true for three random variables, i.e., for…
Md Ashiqur Rahman
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9
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1 answer

How to interpret the direction of the Harvey-Collier test and Rainbow test for linearity?

I implemented both those tests with R, using the lmtest package. Both tests directionally say the same thing (I think) with a very similar p-value of very close to 0. But, are those tests saying that the underlying regression model's residuals are…
Sympa
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6
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1 answer

How to decide the best form of BMI used in cox regression, categorical or continuous?

BMI is always analysed in the form of a categorical variable in medical research. In my Cox regression model, I kept BMI in its original form, i.e., a continuous variable. But the reviewer asked how I can be sure that continuous BMI fits better than…
Zhoufeng
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6
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1 answer

Cox PH linearity assumption: reading martingal residual plots

According to a lot of ressources about Cox PH model, continuous numeric variables should be tested for linearity assymption by plotting the Martingale residuals. In R, you can use survminer::ggcoxfunctional() to easily plot these residuals for the…
Dan Chaltiel
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5
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1 answer

Ways of Testing Linearity Assumption in Multiple Regression apart from Residual Plots

I was going through the assumptions of linear regression and of course one of them was linearity between the dependent and the independent variables - to be precise I should say that the assumption is the conditional mean of $Y_i$ given $X_i$ is…
ALEX.VAMVAS
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5
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Does the Box Tidwell test for linearity of the logit require predictors to be in the range [0,1]?

Given a multinomial logistic regression model with 4 independent variables, 4 relevant interactions and a dependent variable with 3 categorical outcomes, I wanted to test for linearity of the logit. R told me, it is always a good idea to scale the…
Simeon
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3
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1 answer

Correlation = 1 with three random variables

Let $A, B, C$ be random variables with covariance $cov(A B) = 0$ and correlation $corr(B, C) = 1$. Is it true that $cov(A C) = 0$?
Luca Gi
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3
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2 answers

What is relation betwen linearity assumption in OLS and L in BLUE (i.e. OLS is BLUE)

The linearity assumption says that the dependent variable is linear in parameters. When Gauss-Markov assumptions hold, OLS is BLUE, meaning smallest variance amongst Linear Unbiased estimators, where Linear means the OLS estimators, which produce…
user497996
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3
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2 answers

Cox PH model: managing continuous variables and linearity assumption

In an epidemiological study, I'm using martingale plot to assess the linearity of continuous variables. Here are the Martingale Residuals (from Null Model) using R's survminer::ggcoxfunctional() output for 2 variables, on which we see that the…
Dan Chaltiel
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3
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2 answers

Convexity, linearity and their combination for MLE

I'm going through Murphy's ML a Probabilistic Perspective book and in chapter 9 we have the following excerpt talking about the MLE of exponential family distributions: My question is: How do we arrive at the conclusion that because -A(θ) is…
Bar
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3
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Pregibon test for linearity vs. Ramsey's RESET test

Does every Ordinary Least Squares (OLS) regression model have to pass both the Pregibon Test for Linearity (sometimes called link-test) and the Ramsey RESET tests? I am working on an OLS model and it passes the Pregibon test when I include all the…
yellowcap
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3
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reconciling Linearity and Multicollinearity assumptions in ANCOVA

For ANCOVA, many textbooks and other resources require, among other assumptions, that covariates be linearly related to the dependent variable, which makes sense. However, many of the same sources require that pairs of covariates should also be…
JohnCH
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3
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2 answers

Interpreting linearity in residual vs. fitted plot

I am working on a linear regression model and I am not sure how to interpret the following residual vs fitted values plot. For all I know residuals are supposed to fluctuate randomly around 0 which I would say is what my data does more or less (at…
Wiebi
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2
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Assumption logistic regression: linearity of independent variables and log odds?

I checked whether in my logistic regression models the assumption of linearity between the independent variables and the log odds is met. I used R and followed the instructions on this website to do so:…
Franziska
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