# Questions tagged [linearity]

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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, ...
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### 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 ...
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### 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 ...
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### 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.
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### 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 ...
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### 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, ...
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### 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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### 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 ...
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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### 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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1 vote
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 ...
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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 ...
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### 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 ...
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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 [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 ...
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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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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?
1 vote
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 ...
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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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### 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?
1 vote
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 ...
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1 vote
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 ...
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 ...
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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 ...
1 vote
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 ...
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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 ...
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 ...
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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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### 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 ...
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 ...
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 ...
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