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A few paths in path analysis violated linearity assumption, but other paths met the linearity assumption

I'm running a path analysis of serial mediation. Upon checking the linearity assumption, I found that a few paths do NOT have linear relationships, as indicated by rainbow tests and crPlots. However, ...
Dale's user avatar
  • 161
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0 answers
13 views

Cubic splines for Cox models

I have a question about cubic splines. I want to be sure that I understood correctly. When I perform a Cox model with proportional hazards, if I insert continous variables in the model I have to check ...
user99751's user avatar
  • 179
14 votes
4 answers
741 views

Cubic splines in Cox model

I have a question about the cubic splines used in the Cox model to test the linearity for the continuous variables. I read that usually the knots chosen are the quantiles. Can you find different ...
user99751's user avatar
  • 179
3 votes
1 answer
169 views

Non-indicator variable

In OLS regression, do the control variables need to have linear relationship to the dependent variable (linearity assumption) or just the independent/explanatory variables? Thank you.
brian's user avatar
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1 vote
0 answers
26 views

Calculating Expectation using the Linearity of Expectation law and sum of indicator random variables

I'm attempting to complete the problem sets for the Stanford CS109 Statistics course from 2021 as I follow along with the lectures. I'm stuck on a particular problem in one of these problem sets. I ...
fragorl's user avatar
  • 111
3 votes
0 answers
54 views

Checking the linearity assumption in multiple regression

If I wanted to check the mentioned assumption, it is quite easy for only 1 predictor, but what if I have several? I read online that I can plot the residuals vs predicted and see there is no pattern, ...
WalaWizon's user avatar
  • 103
1 vote
0 answers
39 views

An example of a random variable $y\in L^\dagger_2$ having more than one linear combination, $y = \Sigma_{i}\alpha_i x_i = \Sigma_{i}\beta_i x_i$

In the answer for the following exercise: Let $\{x_1,...,x_n\}$ be a finite collection of random variables with $E(x_i^2) \lt \infty$ ($i = 1,..., n$). Show that the set of all linear combinations $\...
Tran Khanh's user avatar
1 vote
1 answer
47 views

Doubt on checking linearity assumption in a mixed-ANCOVA design

I am a PhD student and I have to run a mixed-ANCOVA on some questionnaire scores (my dependent variable) according to the following model. Factors of ANCOVA are (a) Timepoint (pre-intervention, post-...
Fil's user avatar
  • 121
0 votes
0 answers
16 views

Test Linearity Assumption - Hayes PROCESS

Before running the Hayes PROCESS for my moderated mediation, I would like to ensure first, that the linearity assumption is fulfilled. However, at this point, I am not sure which variables need to be ...
ber1495's user avatar
  • 57
2 votes
1 answer
515 views

How to Check Linearity Assumption in Logistic Regression with a Large Dataset?

I am working with a very large dataset that essentially covers the entire population of interest. I want to assess the linearity assumption between an independent variable and the log(odds) of the ...
LeterPeko's user avatar
1 vote
0 answers
74 views

Upward trend in Residuals vs. Fitted - Violation of linearity?

I am currently working with longitudinal data using a linear mixed model (lme4 R package). The linearity plot (fit with ...
a.henrietty's user avatar
5 votes
4 answers
674 views

Provide an intuitive example of the linearity of expectation

Can anyone explain the linearity of expectation in an intuitive way? I have been trying to understand this for far too long now. Please don't use any equations and such, try to use real world examples ...
Jeygopi's user avatar
  • 99
1 vote
1 answer
94 views

How to interpret scatterplot to test linearity b/w covariate and DV?

I'm doing an ANCOVA on a fictitious dataset of math test results (DV) by group (n1 = 50 online training; n2 = 50 no training) with previous math ability as a (covariate) to see if there is a ...
Yael G.'s user avatar
  • 11
3 votes
3 answers
452 views

Continuous predictor variable has non-linear association with log odds of response

I'd like to know if a continuous predictor variable (sal) predicts a binary response (empty) in a logistic mixed effect model, but discovered there is a non-linear relationship between the predictor ...
Nate's user avatar
  • 1,641
3 votes
1 answer
852 views

Testing the linearity assumptions for categorical predictors

Me and my friend are currently writing our final essay but we are having some problems with our analysis… We are doing an hierarchical multiple regression, and we has some categorical predictors (like ...
Wilma J's user avatar
  • 33
1 vote
1 answer
641 views

Interpreting QQ plot

Can we say that the assumption for linearity is met? I'm confused because the tails are heavy, and deviations have a bow-shaped pattern. Still, I think that the linearity has met because the majority ...
Dan's user avatar
  • 11
0 votes
0 answers
2k views

How to interpret Box-Tidwell p-values when sample size is large?

I have a dataset of 300 independent variables and 120,000 observations for which I will perform a binary logistic regression on my dependent variable. Because of the linearity assumption between the ...
Jim R.'s user avatar
  • 53
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0 answers
35 views

Is this relationship between variables linear?

I have four research questions and all of them has the same main "independent variable", as such the relationship between x and y1, y2, y3, y4. This is not a multivariate analysis, I am just ...
LKho's user avatar
  • 63
1 vote
1 answer
156 views

Monotonicity test for multivariable regression

I have dataframe as follow: ...
S. Jeon's user avatar
  • 35
0 votes
1 answer
118 views

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 ...
epalto's user avatar
  • 33
5 votes
1 answer
119 views

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's user avatar
  • 252
0 votes
0 answers
25 views

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(...
Tanner Phillips's user avatar
1 vote
0 answers
57 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.
Pita Fouta's user avatar
1 vote
0 answers
53 views

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 ...
Christian F's user avatar
0 votes
0 answers
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 ...
Wong's user avatar
  • 47
6 votes
1 answer
474 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 ...
Zhoufeng's user avatar
  • 143
1 vote
1 answer
893 views

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 ...
Ola_88's user avatar
  • 93
1 vote
0 answers
299 views

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 ...
Jiaming He's user avatar
17 votes
1 answer
1k views

An Unexpected Expectation!: Does linearity of expectation break for three variables?

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 ...
Md Ashiqur Rahman's user avatar
0 votes
1 answer
565 views

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 ...
Charge's user avatar
  • 65
1 vote
1 answer
236 views

Difference between Dickey-Fuller test and testing for linearity [duplicate]

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 ...
randomwalker's user avatar
0 votes
0 answers
442 views

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 ...
Tiesse's user avatar
  • 23
1 vote
2 answers
3k views

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?
freakazoid's user avatar
1 vote
1 answer
3k views

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 ...
Leo's user avatar
  • 11
0 votes
0 answers
1k views

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 ...
pche3675's user avatar
0 votes
1 answer
614 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?
Chris's user avatar
  • 1
1 vote
0 answers
184 views

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 ...
Christa's user avatar
  • 11
1 vote
0 answers
546 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 ...
João Vitor Gomes's user avatar
0 votes
0 answers
22 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 ...
user584534's user avatar
2 votes
0 answers
552 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 ...
Franziska's user avatar
1 vote
0 answers
844 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 ...
abalter's user avatar
  • 1,138
0 votes
1 answer
397 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 ...
Beat Johner's user avatar
0 votes
0 answers
290 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 ...
FeWa's user avatar
  • 1
2 votes
0 answers
156 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 ...
J3soon's user avatar
  • 121
2 votes
1 answer
118 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 ...
Semoi's user avatar
  • 751
0 votes
0 answers
151 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 ...
badavadapav's user avatar
0 votes
0 answers
98 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 ...
Koh Heebyung's user avatar
0 votes
0 answers
112 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 ...
Guilherme Marthe's user avatar
1 vote
3 answers
3k 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 ...
user250537's user avatar
0 votes
1 answer
429 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 ...
maS's user avatar
  • 139