Questions tagged [linearity]
The linearity tag has no usage guidance.
56
questions
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0answers
39 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 ...
16
votes
1answer
826 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 ...
0
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1answer
39 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 ...
0
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1answer
31 views
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 ...
0
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0answers
15 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 ...
0
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2answers
110 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
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1answer
96 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 ...
0
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0answers
8 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 ...
0
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0answers
143 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 ...
0
votes
1answer
86 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?
1
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0answers
65 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 ...
0
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0answers
105 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 ...
1
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0answers
107 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 ...
0
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0answers
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 ...
2
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0answers
156 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 ...
0
votes
0answers
26 views
Linearity Assumption in Logistic Regression [duplicate]
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 ...
0
votes
0answers
180 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 ...
0
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1answer
109 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 ...
0
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0answers
81 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 ...
1
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0answers
39 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 ...
2
votes
1answer
38 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 ...
0
votes
0answers
50 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 ...
0
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0answers
67 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
...
0
votes
0answers
49 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 ...
0
votes
3answers
478 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 ...
0
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1answer
78 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 ...
0
votes
1answer
93 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 ...
0
votes
1answer
123 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 ...
0
votes
1answer
221 views
Model assumption of linearity
I am trying to interpret the outcome of a test for assumption of linearity. This is the dataframe:
...
0
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0answers
69 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 ...
2
votes
1answer
77 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 ...
2
votes
0answers
104 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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0answers
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 ...
1
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0answers
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 ...
5
votes
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 ...
1
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0answers
216 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 ...
5
votes
1answer
2k 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 ...
3
votes
2answers
1k 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 ...
1
vote
1answer
99 views
Violation of linearity?
Can anyone tell me if, based on this image, the linearity assumption is violated in my model?
0
votes
1answer
54 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 ...
1
vote
1answer
698 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:
...
2
votes
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 ...
3
votes
2answers
996 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 ...
2
votes
1answer
3k 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 ...
4
votes
0answers
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.
...
2
votes
1answer
341 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 ...
1
vote
1answer
3k 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. ...
3
votes
0answers
164 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 ...
17
votes
2answers
23k 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 ...
2
votes
1answer
542 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?
...
