Questions tagged [nonlinearity]
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65 questions
8 votes
1 answer
91 views
How to uniformly sample from a nonlinearly transformed simplex?
Let $S = \{ w \in \mathbb{R}^3 : w_1 + w_2 + w_3 = 1,; w_i \ge 0 \}$ be the standard 2-simplex. Consider the transformation $$ T(w_1, w_2, w_3) = (w_1, w_2^p, w_3), $$ not followed by a ...
0 votes
0 answers
71 views
Linear regression after multiple imputation: Should assumptions be checked before or after AIC-based model selection?
I’m currently working on multiple regression analyses with a small sample (n = 36), using multiple imputation via the mice package in R (5 imputed datasets). The ...
2 votes
2 answers
583 views
Multiple linear regression homoscedasticity/linearity
My question is about the implications of the violation of homoscedasticity/linearity for multiple linear regression. I have tried to find the answer in multiple sources but could not figure it out. I ...
- 21
3 votes
1 answer
870 views
Splines, logistic regression and sample size considerations
I have around 500 observations with a binary outcome at 25% prevalence and will be building an internally validated prediction model. I want to use splines to model non linearity in my continuous ...
- 31
0 votes
1 answer
256 views
What does it mean when dots on a residual vs fitted graph are clumped like a shotgun result? How do I fix it if it needs to be fixed?
Here's the code for these graphs ...
- 1
0 votes
0 answers
115 views
Is there any approach to know the shape of nonlinear correlation between two variables?
I have read some of the existing non-linear correlation analyses such are Maximal Information Coefficient (MIC) and Distance Correlation, both of them don't tell us about how the correlation is shaped ...
- 51
3 votes
1 answer
228 views
Ramsey RESET Test
The Ramsey RESET test uses the fitted value of y to test nonlinearity, for example: $$ y_i=x_i\beta+\epsilon $$ $$ \hat{y_i}=x_ib $$ $$ y_i=x_i\beta+\gamma\hat{y}^2_i+u_i $$ Test if $\gamma=0$ Why do ...
- 357
2 votes
0 answers
53 views
What is the optimal technique for determining statistical thresholds?
Relevant context: epidemiologists define an outbreak according to six defined stages (investigation, recognition, initiation, acceleration, deceleration, and preparation). From a local perspective, it ...
- 101
1 vote
1 answer
532 views
What is the definition of a non-linear estimator? I heard that ratio of estimators is non-linear
Why don't we consider nonlinear estimators for the parameters of linear regression models? says that LASSO is a non-linear estimator. I think LASSO has a solution via matrix multiplication. I don'...
user318514
1 vote
1 answer
84 views
If all computed features ( or components ) in Neural Network nodes are positive numbers , does using Relu meaningful?
I am trying to understand the following issue. The reason we use activation functions such as sigmoid,tanh or relu in neural networks is to obtain a nonlinear combination of input features ( x's). My ...
- 325
2 votes
1 answer
1k views
Modelling non-linearity for binary independent variables in logistic regression
I have fit a logistic regression where the response variable is binary - whether an interview candidate got the position or not - and the independent variables are a combination of continuous, ...
- 419
9 votes
4 answers
8k views
A linear pattern occurs on my residual plot: what can I do?
I'm a bit stuck with a problem here and any kind of help would help a lot :) Just to give a clue about my data. I have 6 independant variables (IV) which are: $X_1$ = Population -within a block- $X_2$...
- 91
0 votes
0 answers
103 views
Variable relationship case: x1 is not correlated to y but x2 which is related to x1 is correlated to y
I would like to know what is the specific term given to this case, or how is this justified in technical words: x1 is not correlated to y but x2 which is correlated to x1 is correlated to y.
- 111
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 ...
- 77
1 vote
1 answer
589 views
Dataset with low and non-linearly correlated variables: suggestions on modelling strategies
I have a dataset with low and non-linearly correlated variables and I am interested in assessing the relations between the Independent Variable (IV) and Dependent Variable (DV), however I am not able ...
- 163