Questions tagged [linearity]

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13 views

Interpretation of scatter plot - vertical line patter spotted

can I please get quick help on this scatter plot of standardised residuals against predicted values. Does this mean this violated normality, linearity and homogeneity? How should I interpret that ...
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33 views

Relationship between Histogram , Scatter plot , Normality , Linearity

I have the following doubt: suppose you have a categorical variable called 'neighborhood' with 20 categorical levels/values ("vila madalena", "mooca", etc). and I want to check ...
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19 views

Multivariate normal distribution property [duplicate]

The Econonometrics book by Hansen mentions this property of a multivariate normal distribution: If $X∼N(\mu,\Sigma)$ then $AX+b∼N(Aμ+b,AΣA^\prime)$. It goes to say that a simple implication of this ...
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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 ...
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21 views

Linearity Assumption in Logistic Regression

In test for linearity (Box-Tidwell) both continuous IVs were significant (p<.000). I did the natural log transformation and inverse square root transformation and ran it again including the ...
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53 views

How to Assess Linearity assumption of logit in logistic regression

In Applied Lineare Regression, (Hosmer, Lemeshow, Sturdivant 3rd ed.) Ch. 4, they present "Purposeful Selection." Part of step 5 is to assess the validity of the linearity assumption of the logit vs ...
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1answer
65 views

Dealing with violation of OLS assumptions

I am currently writing my Master's thesis in economics. I am analyzing the second home rate in Swiss municipalities in R. The second home rate for municipality $j$ is defined as the share of the ...
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29 views

Mixed Model in R: Test for linearity and inclusion of lagged variable

I have specified a mixed model in R, based on a data set containing advertising awareness as DV and advertising spends as IV. The effect of the advertising spends on awareness is moderated by two ...
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19 views

What is the problem with my Ramsey Test's result?

I run the multiple regression on Stata and now I have to test the linearity of all my independent variables. First, I analyzed the residuals versus predictors and I transformed several variables. ...
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26 views

Prove or disprove the Linearity of Expectiles used in Expectile Regression

For expectation (mean), there are many useful properties such as Linearity of Expectation: $\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]$ $\mathbb{E}[\alpha X]=\alpha\mathbb{E}[X]$ (The 2 equations ...
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27 views

linearity of a measurement device

I like to evaluate the linearity of a measurement system. In order to do so I read ISO 22514-7 as well as Breyfogle's "Implementing six sigma". However, the procedure is still unclear to me. So I'm ...
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26 views

How to test interaction when loglinearity is violated in Cox model?

In a Cox PH regression, I would like to model an interaction between two variables. The problem is that one of the variables breaks the log-linearity assumption. Based on my previous questions (...
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36 views

Why is linearity (as in linearity in BLUE) a desirable property for OLS estimators?

By linearity, I do not mean the linearity of the estimators in the OLS regression equation, what I am trying to ask is why are the beta coefficients a linear function of y(i)'s. Why is linearity a ...
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59 views

Linearity assumption of logistic regression [duplicate]

Do I have to check linearity assumption of logistic regression (Log odds of outcome with continuous variable) using graph of predicted logodds (by logistic regression) and continuous variable Or ...
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46 views

Is there a way to differentiate between linear and non-linear datasets in simulations studies?

I'm trying to find a a measure of "linearity" among different simulated data sets and how I could control for such differences. This idea came from studying Hastie's and Tibshirani's work around ...
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3answers
164 views

Should one drop independent variables if they don't have linear relationship with the response variable?

I am building a linear regression model using Ridge regression. Some of the independent variables don't have linear relationships with the dependent variable. I've tried to do data transformations on ...
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1answer
57 views

Linear regression, linearity assumption violated?

Below i have attached a scatter plot showing my dependent variable on the Y-axis and my independent variable on the X-axis I am not sure if the linearity assumption is violated? Can anyone explain ...
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1answer
58 views

SEM 4 questions - testing linearity, sum score, number of variables, independent variables

For my master thesis I'm making a structural equation model. However, I do not have much experience with this. So here are some different questions. I read that one of the assumptions important for ...
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1answer
73 views

How to check the linearity of continuous variable in linear mixed model

I'm doing a linear mixed model using lme. In my adjustement factors, I have a continuous varaible (named X1). And I want to check the linearity of this variable using a spline function or a ...
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1answer
170 views

Model assumption of linearity

I am trying to interpret the outcome of a test for assumption of linearity. This is the dataframe: ...
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54 views

Is checking for normality and linearity in this way correct?

Testing normality using a significance test is a little bit useless especially when you have a large sample size So, recently I found a way to test normality by running a fake regression using ...
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1answer
47 views

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 ...
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84 views

How do Component + Residual Plots look like in Polynomial Regression?

Components + resiudal plots or partial residual plots can be used to detect deviations from linearity in multiple linear regression. They work by plotting the variable on the x-axis and the component+...
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19 views

linear relationship [closed]

Could the data points fall on the regression line to assume that the relationship is linear, please check the attached photo what if the scatter plot shows that the relationship is linear but the ...
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23 views

Linear Unconditional X-Y, Non-Linear Conditional X-Y

Intuitively, I can imagine that an unconditional (i.e., unadjusted for any covariates) Y~X relation can present as a linear relation, whereas a conditional Y~X|Z relation can present as a non-linear ...
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1answer
1k views

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 ...
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190 views

ANCOVA - Non-linearity of covariate

I have a dataset where I calculated genetic distances between populations of some animals (a continuous variable). I want to know if these differences are explained by physical or/and ecological ...
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1answer
1k views

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 ...
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2answers
724 views

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 ...
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1answer
76 views

Violation of linearity?

Can anyone tell me if, based on this image, the linearity assumption is violated in my model?
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1answer
53 views

Linearity assumption with dependent indicator variable and continuous independent variable?

If i have a regression model with the independent variable as continuous, while my dependent variable is a dummy variable (only one independent variable) then will the linearity assumption hold ...
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1answer
495 views

Diagnosing linearity for multiple regression model

I have the following model in R to estimate the change in mosquito abundance each year when controlling for climate variables: ...
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1answer
2k views

The best way to check the linearity assumption in ANOVA (except using scatter plots)

I was wondering that ANOVA is based on linearity assumption. If Yes, how can I check the linearity between observations. I know using plot would be useful but it is difficult to find the degree of ...
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2answers
780 views

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 ...
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1answer
2k views

Interpretation of residual plot for mixed effect linear model

I am trying to do mixed effect regression model with lme4.lmer function. The model has two fixed categorical variables, one random categorical variable and response is continuous variable (distance in ...
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3k views

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. ...
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1answer
284 views

Problems with zero values when testing for linearity of the logit

From Field's 'Discovering Statistics using SPSS' I read that you should test for linearity of the logit when using a logistic regression. The process explained in the book covers the natural log ...
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1answer
2k views

help for interpreting the residuals vs. fitted values plot

I have an ordinal variable (scale of stress) considered as continuous predictor in a multivariate linear regression. I would like to verify the assumption of linearity and this is my residuals vs. ...
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157 views

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 ...
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17k views

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 ...
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1answer
508 views

When performing a linearizing transformation, do I apply transformation to dummy variables?

Suppose I wanted to transform variables to achieve linearity (e.g.), would I omit the dummy variables from the transformation? ...
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1answer
317 views

Non Linear Regression -Regression Trees

For datasets of higher dimensions, how do I decide if a Linear model is sufficient to fit the data or if I have to use non linear models like regression trees to fit the data ? NOTE:I did try both ...
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1answer
75 views

Is there a test to verify that data is linear or rather logarithmic?

I've done two small experiments, and if I visualize that data, it seems as there is a linear trend in the first one, and a logarithmic trend in the second. Is there a test to verify that this is ...
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299 views

How to graph continuous independent variable and logit of dichotomous outcome in SPSS

First question: I am using SPSS, and I want to graph the logit of my dependent variable on the y axis and my continuous independent variable on the x-axis. I am interested in visualizing the ...
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2answers
2k views

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 ...
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1answer
4k views

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 ...
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769 views

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 ...