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If R2 is not appropriate for non-linear ML algorithms such as Random Forests, can a Pearson or Spearman correlation be used as performance metric?

$R^2$ is not appropriate for non-linear models, such as Random Forest (RFs) models. https://arxiv.org/pdf/1611.03063 Is R-squared truly an invalid metric for non-linear models? https://...
JElder's user avatar
  • 1,037
2 votes
1 answer
35 views

Nonlinear indirect effect in lavaan & semTools

I would like to use semTools to examine several indirect effects. However, some predictors have nonlinear relationships (i.e., quadratic) with the mediators, but I found very little information online ...
Dale's user avatar
  • 161
0 votes
0 answers
31 views

Sufficient number of data to determine whether a model fits the data well

I was wondering if, chosen a proper mathematical model, there is a minimum number of data that allows us to state if the model fits well the data or it doesn't. I'll explain better my question. Let's ...
Mattia's user avatar
  • 1
0 votes
0 answers
10 views

How to interpret Diffusion Maps for the iris dataset?

This might be a poor exercise but I'm trying to understand the methods of paper and if it makes sense to adapt my linear-based workflow with PCA to non-linear manifold methods; thought trying out ...
O.rka's user avatar
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0 answers
27 views

OLS and Linear and Nonlinear Models

I understand what linear (w.r.t. coefficients) models are. For example, the power model $Y=k X^p$ is nonlinear..$Y= \beta ^X$ is also nonlinear, etc. Ordinary-least-squares (OLS) is one of the many ...
Brett Cooper's user avatar
0 votes
0 answers
21 views

Identifications for the linear and non-linear models

Consider a linear model and a non-linear model: $$Y=X'\beta+u$$ $$Y=m\left(X;\beta\right)+u$$ Then, in my understanding, the identification conditions for $\beta$ in the linear model are Condition 1: ...
MinChul Park's user avatar
3 votes
1 answer
30 views

Nonlinearity of model using Sobol indices

I'm analyzing a computationally demanding numeric model where I want to show that nonlinearities play a certain role for my problem. I want to do this using Sobol sensitivity indices of first oder by ...
Sobol's user avatar
  • 41
5 votes
1 answer
115 views

How to estimate this specific logistic regression model which is not linear in its parameters?

A. Suppose I want to fit the regression $Y = f(\lambda X_1 + (1-\lambda) X_2)$ where $f(x) = ax^2 + bx + c$, and $\lambda$, a, b, c are to be estimated using the data. This is nonlinear, but it's ...
Mohan's user avatar
  • 939
1 vote
0 answers
66 views

crossed random effects in nonlinear mixed-effects model

I am a beginner in mixed effects modeling and am trying to find some useful code to solve my current problem. Specifically, I'm having some problems with model fitting. I'm looking for a ...
Duochishuiguo's user avatar
1 vote
1 answer
80 views

Interpertation of a conditional quadratic latent growth curve model (i.e., with predictors)

I have a conditional quadratic latent growth curve model and am wondering how to interpret the results. My predictor of interest is significantly associated with the slope factor (B = -0.45, p = .001) ...
Aepkr's user avatar
  • 309
0 votes
0 answers
346 views

How to calculate covariance matrix in nonlinear least squares

I am fitting a nonlinear model to observations by using least squares to estimated the model parameters. Theoretically, the covariance matrix of the parameters can be estimated by inverting the ...
GreatJourney's user avatar
1 vote
1 answer
79 views

Specifying continuous autoregressive covariance structure in multilevel daily diary model

I have a daily diary dataset with daily ratings of mood (e.g., daily rating of happiness) between two treatment conditions. The complete number of days of ratings vary widely across participants and ...
stilesb's user avatar
  • 31
1 vote
1 answer
68 views

Can All Regression Supervised Machine Learning Models Be Viewed as Linear Models Over Transformed Features?

I've been studying various supervised machine learning algorithms for regression tasks, and I've come across an interesting perspective suggesting all machine learning models could be represented as ...
alejandroll10's user avatar
1 vote
0 answers
34 views

Regression model : does non-linearity imply interaction effect?

I would like to know more on the relation between non linearity and interaction effect. For example, if we have a linear model of the form $$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon $$ we ...
G2MWF's user avatar
  • 111
0 votes
0 answers
158 views

Multiplicative linear model

I am considering the model: $$ y_t = \beta_0\left(\Pi_{i=0}^{K}x_{i,t}^{\beta_i}\right)\left(\Pi_{j = K+1}^{L}e^{\beta_{j}x_{j,t}}\right) $$ where we want to have multiplicative effect between ...
G2MWF's user avatar
  • 111
4 votes
1 answer
160 views

Can nonlinear regression identify this equation?

I want to estimate the following regression equation: $y = a + \frac{b}{r*x + 1}$ x is the independent variable, and a, b and r are parameters to be estimated. I have been told that the model is not ...
William Foley's user avatar
1 vote
0 answers
27 views

Are polynomial models unreliable at data extremes? [duplicate]

I have fitted a polynomial regression (4 degree model) to describe a non-linear relationship between my two variables. My question is why does this model begin to decrease towards the right hand side ...
Pat Taggart's user avatar
3 votes
0 answers
700 views

Why do you take the natural logarithm plus one? [duplicate]

I have read in many different studies now that take the natural logarithm of one plus x. For example, in econometrics many studies use the natural logarithm of one plus the total assets. I do not ...
Limps's user avatar
  • 41
1 vote
1 answer
102 views

Non-Normal Residuals in Real World Data

I have a dataset that includes real world data (not experimental or survey data) for a set of countries year by year for 40 years. The data was collected by entities such as the World Bank and United ...
Tom's user avatar
  • 11
2 votes
0 answers
13 views

What would be a good model fit for a rise-and-fall time series data?

I have two time series measurement of protein "activation" under two different conditions, (A) and (B). My end goal is to fit a model and use the model parameter that best describes the rate ...
jack kelly's user avatar
1 vote
1 answer
633 views

Interpretation of multilevel negative binomial output

I am wondering how to interpret the coefficients returned in a multilevel (repeated measures nested within person; random intercepts-only) negative binomial regression. Output is pasted below ...
stilesb's user avatar
  • 31
2 votes
1 answer
95 views

Linear regression expression of a non-linear model

$Y=\frac{x_1x_2}{β_0+β_1x_1+β_2x_2}$ It was written on some slide of my econometrics class that such a model could be expressed in the form of a linear model, but I am struggling to derive it by ...
toto2594's user avatar
3 votes
1 answer
674 views

Are ARCH and GARCH linear or non-linear models?

Are these models considered linear models? I was reading an article that stated that GARCH(1,1) is superior to non-linear GARCH Models. Source: https://www.researchgate.net/publication/...
Tiago Pratas's user avatar
1 vote
1 answer
331 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'...
user avatar
0 votes
1 answer
77 views

Power calculation by simulation - what do I do with model failures?

I'm trying to run a power calculation by simulation on a set of exponential decay datasets using the nlme package in R. Here's the process: Simulate a bunch of exponentials, using some conservative ...
Piethon's user avatar
  • 111
0 votes
1 answer
126 views

Transformation of periodic data prior to PCA?

Basically I have periodic data (angles from -180 to 180) that I want perform a PCA on. However, since the data is periodic, a change in angle from say 170 to 10 will not be accurately reflected. I was ...
Yousuf Khan's user avatar
3 votes
1 answer
88 views

Can Correlation based feature selection discard features that show no correlation by themselves but are meaningful only if combined?

Assuming a feature selection process based on correlation or some other metric, is it possible to overlook input features that by themselves show no actual correlation with the target values, but that ...
VoteAnthony's user avatar
1 vote
0 answers
19 views

Mapping Parametric Curves with auxiliary variables

The image below displays an approach of using an auxiliary variable to map the parametric curves of a standard normal pdf and cdf. In Equation (1), z as r.v. is clearly one-dimensional. However, after ...
Blackforest95's user avatar
1 vote
0 answers
678 views

Using curve_fit for Non-Linear, Multi-Variate Models [Python] [closed]

Warning: ML Noob. I have a 3D dataset (data at the bottom) with 2 feature variables and 1 target variable. Polynomial Regression produced unsatisfactory results and it seems that the relationship of ...
Austin Prater's user avatar
1 vote
0 answers
40 views

How to test a product of a OLS estimators?

I estimated a vector $\beta $ using OLS $\hat \beta =(\hat e_1 \hat e_2 \hat e_3)$ and I have the covariance matrice $\hat v(\hat \beta )$. How can I test this null hypothesis $H_0 : \hat e_1 \hat ...
wageeh's user avatar
  • 241
2 votes
1 answer
524 views

Is Ordinal logistic regression linear or nonlinear?

Quick question, is ordinal logistic regression a linear or nonlinear model? Finding different sources supporting the other, and the more I read the more I get confused myself. Perse, it should fall ...
Moa Herrgård's user avatar
0 votes
0 answers
22 views

Advice on fitting curve to three-pooled plant decomposition model in r

I have just finished running a plant decomposition experiment measuring the decomposition of pine needles across climate and lithological types. We have mass loss, plant chemistry data (c, n, labile ...
Daniel Fishburn's user avatar
0 votes
0 answers
70 views

Need a predictive (binary outcome) model for a set of binary variables and one continuous variable

I have a data set of about 1600 binary results, that I want to predict from 9 binary variables and a continuous variable. The relationship between the continuous variable and the result variable by ...
user2246336's user avatar
0 votes
1 answer
117 views

Fitting a cubic-like curve to data in R

I tried using nls() in R to fit the following expression to a set of data: where g=9.8, alpha & B_0 are unknown, a = 0.01, z_0 = 0.3 such that: theory <- as.formula(V~-(9.8)ab*(pi)(0.02^2)(T)(...
SomberTheScrub's user avatar
0 votes
0 answers
24 views

Distribution of product of samples from two Normal distributions [duplicate]

Hello! I have two normally distributed random variables $M \sim N(\mu_1,\sigma_1^2)$ and $V \sim N(\mu_2,\sigma_2^2)$ having physical meaning as $M$ - mass and $V$ - volume. I need to figure out the ...
Andrej Kružliak's user avatar
1 vote
0 answers
54 views

Additive error model for non-linear case

I have checked other questions regarding additive noise model, but I could not convince myself for non-linear case. Assume the data vector $\mathbf{d}$ is described by a possibly non-linear ...
T. B.'s user avatar
  • 11
0 votes
1 answer
77 views

Kaplan's Non-Linearity Test

I've been searching for an R package or function that applies the Kaplan non-linearity test to univariate time series but they are nowhere to be found. Such test has been widely applied in the ...
Blg Khalil's user avatar
1 vote
1 answer
765 views

Possible non-linearity pspline Cox model

Our working group ran a Cox regression with a p-spline to model the possible non-linearity of continuous variables. However, I'm a bit confused with the interpretation of the linearity or non-...
psoares's user avatar
  • 606
7 votes
2 answers
1k views

How to fit logistic regression to circular data?

I've made a script that can do normal logistic regression with sigmoid(linear model). However, I have data that has a circular decision boundary and looks like this. My question is how I can modify ...
Eirik's user avatar
  • 71
1 vote
0 answers
158 views

Degrees of freedom for a $\chi^2$ with non-linear polynomial model

I have a $\chi^2$ below for some model function $F$: $$ \chi^2 = \sum_{i=1}^{i=M} \frac{\left(y_{i}-F\left(x_i;\vec{a}\right)\right)^2}{\left(\Delta y_{i}\right)^2} $$ I know that non-linear model ...
Craig's user avatar
  • 143
2 votes
1 answer
96 views

If X^2 is not significant but X is significant, do I have to remove X^2 and run again the regression analysis?

Model DV ~ W+PDSR+Corr+(FAGDP1+FAGDP2)+log(PCGDP)+Exp+Pop+Health FAGDP2=FAGDP1^2 Result: After removing FAGDP2(FAGDP1^2) from the model, FAGDP1 turns to be insignificant Am I right in removing FAGDP^...
amnay mehlaoui's user avatar
13 votes
2 answers
7k views

RMSE vs MSE loss function - the optimization solutions are equivalent?

If we optimize a function $f$ with respect to loss $L$, which is defined as RMSE; Are we going to get the same solution as optimizing MSE ? Even, if the function $f$ is non-linear (e.g. a neural ...
Daniel Wiczew's user avatar
1 vote
0 answers
652 views

Quantile regression with an exponential function

The following equation: y = a*x**b where y is a nonlinear function of x. By taking logs, the equation can be expressed as: ln(y) = ln(a) + bln(x). I would like to run a quantile regression instead of ...
user3527227's user avatar
0 votes
0 answers
299 views

standar error of non-linear regression

I'm trying to compute the standar error of a non-linear regression fit, I find the answer in this post Non-linear regression confidence interval But i did't find that formula in any other place,and I ...
Eric Cardozo's user avatar
1 vote
0 answers
16 views

"Nonlinear" random spatial field: an example

I want to generate a "nonlinear" random spatial field in the sense that the autocorrelation function in function of the lag/distance $h$, $\rho(h)$, should be not equal to the $R(h)$ ...
Massimiliano Romana's user avatar
1 vote
2 answers
661 views

Isn't ReLU just a linear function? [duplicate]

I am doing Andew Ng's Deep Learning course and he says that ReLU is better than Sigmoid, but it makes no sense to me at all. The biggest advantage of activation functions are too get a non-linear ...
Mr. Johnny Doe's user avatar
2 votes
1 answer
146 views

Proof of how to calculate the coefficient of variation of a nonlinear function

I'm struggling to find the proof of Eq. D.14b shown in the figure below: The variable $b$ represents the “Least Squares” best-fit to the slope between $r_e$ and $r_t$ which both depend on $X_1$ to $...
jpcgandre's user avatar
  • 413
1 vote
0 answers
117 views

Why do we use Relu if it's mostly linear

We use activation functions in neural nets to introduce some non-linearity. Now I understand that Relu is a non-linear function and I had no problems with it. But today I learned that when the output ...
diane's user avatar
  • 43
1 vote
0 answers
20 views

Simultaneous interaction model with nonlinear equations

I observe many groups of 3 individuals, and I want to estimate an interaction model of the form: $$\begin{array}{rl} y_1&=f_1(x, y-1)+e_1\\ y_2&=f_2(x, y-2)+e_2\\ y_3&=f_3(x, y-3)+e_3 \end{...
Margherita Comola's user avatar
3 votes
1 answer
244 views

Non-normal data transformation - what does it imply exactly and what does my results mean?

I am missing some understanding here. I am inspecting the relationship between the heart rate variability (HRV) and errors in the Sustained Attention to Response Task. When I conduct a basic linear ...
timothy's user avatar
  • 77

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