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# Questions tagged [nonlinear]

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2 answers
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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://...
• 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 ...
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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 ...
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 ...
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0 votes
0 answers
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### 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 ...
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: ...
• 401
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 ...
• 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 ...
• 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 ...
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) ...
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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 ...
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 ...
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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 ...
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 ...
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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 ...
• 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 ...
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 ...
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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 ...
• 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 ...
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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 ...
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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 ...
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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 ...
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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/...
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'...
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 ...
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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 ...
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 ...
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 ...
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 ...
1 vote
0 answers
40 views

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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 ...
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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{...
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 ...
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