Questions tagged [linearity]

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Variable selection in ordered ordinal model - transform variables prior?

I am running a series of proportional odds ordinal models. I have a set of predictors that correlate. I aim to find out how effect sizes and significance change after introducing control and ...
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Linear regression has good performance in validation set despite not meeting the linearity assumption

I have a dataset with about 8000 samples and 18 predictors (16 continuous, 2 categorical). I am trying fit a linear regression, but despite trying multiple transformations, I can't make it meet the ...
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Closed-form solution of logistic regression [duplicate]

"For logistic regression, there is no longer a closed-form solution, due to the non-linearity of the logistic sigmoid function". Can someone please explain the above quoted sentence in ...
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3 votes
1 answer
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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 $cov(A C) = 0$?
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Prove linearity of impulse response model

Given the following time varying model: $Z(t) = \alpha*t*Z(t-1)$, how do I go about proving linearity? If you simplify based on some constant at Z(0), you get the general solution $ Z(t) = \alpha^tt!Z(...
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I only have binary independent variables in OLS - how can i test for linearity?

I have created an OLS regression model, to predict the change in consumers prices at fast-food restaurants and all of my independent variables are binary (either 1 or 0), for convenience i have ...
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1 vote
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45 views

OLS linearity assumptions

Do we have to check on stata that the OLS assumptions of linearity of a regression if the regression is already linear in parameters? I'm having trouble with this concept. Thanks in advance.
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Is it ok to drop a non-linear treatment level in ANCOVA?

I am running an ancova to measure differences in an allometric relationship between tree height (dependent variable) and diameter (covariate) among one nutrient treatment with 4 levels. One of the ...
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42 views

Find Positive Association and Negative Association Between 2 Categorical Variables

I have different employees’ performance rating data( low, mixed, strong, significant, exceptional) in 1 column and certain commonly occurring words used in their performance reviews encoded as 0 and 1 ...
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Why doesn't a residual plot indicate whether or not the linearity assumption is violated?

I learned in stats that a residual plot is a plot of the residuals on the vertical axis and the independent variable on the horizontal axis. So basically it looks like the regression line turned ...
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39 views

Exploring relation between x and y [duplicate]

While there are numerous methods in exploring relation between x and y upon receiving a new dataset. Yet it seems I can't find any conclusive guide as of the sequence of analysis, e.g. do correlation ...
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6 votes
1 answer
243 views

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 ...
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Assumptions of linearity and homoskedasticity when the DV is a Likert scale - how to interpret the (optimized) residual plots?

I am currently building mixed models for several analyses where each the DV is ordinal, specifically a 7-point Likert scale. Now, I am fully aware of the controversies of using Likert scale as a DV ...
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Can someone clarify what the linear assumption of PCA is?

For the past few hours I've been trying to search what this linear assumption is. Some of the articles states that that your independent variables have to be linear in relationship and need some type ...
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16 votes
1 answer
938 views

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 ...
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linearity in parameter assumption - implication for the Gauss-Markov theorem [closed]

Even if a similar question has been asked many times, I have not been able to understand the consequences of non linearity in parameter in relation to the Gauss-Markov theorem. In this question ...
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Difference between Dickey-Fuller test and testing for linearity

The Dickey-Fuller test tests an AR(1) series for stationarity. An AR(1) series can be written as: $x_t = \phi x_{t-1} + \epsilon_t $ with $\phi$ constant and $\epsilon_t $ white noise. The series is ...
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Box-Tidwell of same variable in two different logistic models

I'm running two identical logistic models on two different (and with mutually exclusive 1's) DVs on the same dataset. I have an independent variable with similar coefficient in both models and I ...
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2 answers
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Assumption of linearity between variables and log odds in logistic regression

I know that in logistic regression we assume a linear relationship between the independent variables and the logits. Can you explain why is this a reasonable assumption?
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1 vote
1 answer
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Solution in case of violation of the linearity assumption in the logistic regression model? (possibly in R)

I have a problem with my logistic regression that I set up and I hope someone can help me. (I am working with R) My data is based on hourly values. The dependent variable is a dichotomous variable (1 ...
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Valid alternative to Box Tidwell method for Linear Regression [duplicate]

I am building a Logistic Regression model (in sklearn) and want to verify that the assumption regarding the linearity between X and the logit function is correct. I am using Python so am looking for ...
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1 answer
259 views

How to test linearity in ordinal logistic regression analysis?

One of the assumptions for performing ordinal regression is linearity. How to test this for this specific type of regression? Do you have to use logit etc.? And how does this work in SPSS?
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Does this scatter plot suggest non-linearity?

As part of assumption testing for ordinary least squares (OLS), I am examining the linearity between the variables in my model. I'm using scatterplots between the independent variables (IVs) and ...
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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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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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2 votes
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351 views

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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402 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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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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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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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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2 votes
1 answer
70 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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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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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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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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3 answers
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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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0 votes
1 answer
163 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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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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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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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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90 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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3 votes
2 answers
276 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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2 votes
0 answers
127 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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1 vote
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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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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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5 votes
1 answer
2k 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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1 vote
0 answers
283 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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6 votes
1 answer
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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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3 votes
2 answers
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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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1 vote
1 answer
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Violation of linearity?

Can anyone tell me if, based on this image, the linearity assumption is violated in my model?
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1 answer
61 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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