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Use this tag only for regression models (q.v.) in which the response is a nonlinear functions of the *parameters* (not because it's a nonlinear function of the *predictors*).

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54 views

General restriction for covariance matrix in multivariate normal distribution

Suppose we look at the following model $$ \vec y_i=\vec\mu_i + \vec\epsilon_i, \qquad \vec\epsilon_i\sim N(\vec0, \Sigma) $$ where $\vec y_i$s is observed, $\vec\mu_i$s are known, and $\vec\...
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0answers
8 views

Anova test with quantile regression model

I want to create a anova test with two or more non-linear quantile regression models: ...
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0answers
21 views

how to train model with features have low variance in train set

Assume that I trained a nonlinear model , one feature of the training data has very low variance, because of this, the same feature of the test could be quite different, at least in scale, from the ...
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0answers
53 views

Fitting Data to an Unknown Distribution

Consider a sample $x_1,\ldots,x_n \sim F$ from an unknown parametric distribution where $F$ is the cumulative distribution. We observe data in the form $F(x_1),\ldots,F(x_n)$. Stated differently, we ...
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1answer
26 views

Nonlinear least squares transformation

Suppose that I wish to estimate the parametes $\alpha$ and $\beta$ in the following regression model: $$ Y=K^{\alpha}L^{\beta}\epsilon $$ A standard procedure is to take logs and estimate $$ \text{...
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22 views

Power Regression with multiple variables

I have conducted a parametric study and have obtained a dataset. $Y$ is the independent variable and $X_1$, $X_2$ and $X_3$ are the three independent variables. Now, looking at the problem, I felt ...
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0answers
29 views

estimating regression function by approximation

Suppose I have data $(Y_i,X_i)_{i=1}^n$ with a following regression model $$Y_i = f(X_i) +\varepsilon_i $$ The goal is to estimate $f(X_i)$. I do not want to use Nadaraya-Watson method. Rather I ...
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0answers
77 views

How to fit exponential y=A(1-exp(B*X)) function to a given data set? Especially how to determine the initial start parameters? [duplicate]

I have a data set in which $y$ is roughly related to $\log(x)$. Now I wish to fit the curve $$y=A(1-\exp(BX))$$ When I use R and the nls2 function, then I ...
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0answers
29 views

What are the errors of the coefficients of a quadratic regression?

I have performed a quadratic regression in order to determine $y = a\cdot x^2 + b \cdot x + c$ by following the steps depicted in the section 'Find by Hand' in http://www.statisticshowto.com/...
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0answers
47 views

Theoretical premise of averaging / taking median of non-linear regression coefficients

I recently read: Is there any theoretical problem with averaging regression coefficients to build a model? and was intrigued as it brings a basic machine learning concept to good old fashioned OLS. ...
3
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1answer
48 views

Can I still use Linear Regression assumptions test on a linear model with a Polynomial variable

I have a multivariate linear model (y=x1+x2) which gives me the following results when using R's plot() function: I can clearly see that the Normality and ...
1
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2answers
49 views

Time Series: use of Box-Cox to reduce the “noise”

I am researching the best method to use with time series. FBprophet (Python) seems like a strong option. To prepare time series for Prophet I am thinking about using boxcox and inv_boxcox at the end ...
2
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0answers
25 views

How to Estimate a Multi-variable Harmonic Function on a Grid?

What estimation schemes do you suggest for solving the following discrete problem: $$y=f(X)+\epsilon,\\$$ $$\Delta f=0.$$ Here, $X=(x_1,\cdots,x_p)\in\mathbb{R}^{p}$ and $\Delta=\sum_{i=1}^p \frac{\...
2
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0answers
52 views

Fitting a sinusoidal curve only with max-min values

I have a series of high-low tide values, approx. every 6h, and each one has the corresponding time. I would like to get (an estimation of) the values between each record. I was thinking I could create ...
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0answers
17 views

Calculating proportion of variance explained for single variables in multivariable non linear models

I have a non linear model with two predictor variables. Is it possible to calculate the proportion of variance explained by each of the two predictor variables?
2
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1answer
70 views

Working out error on fit parameters for nonlinear fit

I am struggling to find a concrete formula for the Hessian or Jacobian in respects to fitting parameters. I have implemented some fitting in Java using the Apache Common Maths package for the ...
2
votes
1answer
43 views

Would it be possible to have a time series which has zero-mean but is not stationary?

E.g. $ y_t= A_1y_{t−1} + u_t, u_t ∼ (0, \Sigma_u)$ Would it be possible to let the time series to have zero-mean but is not stationary?
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0answers
11 views

Specify a product of predictors In a nonlinear Model Formula

I am trying to estimate the parameters of a non-linear model using MLE in R y = $a_x$ + $b_x$$k_t$ where x and t are factors (with unequal levels). I found out that using the ...
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0answers
34 views

Is it possible to fit a given function to a data set to improve the function form?

I have a function and I know how to obtain numerical solutions, how to make a non-linear fitting to obtain each point that want and etc.. What I want to know is if there's a possibility to improve to ...
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0answers
18 views

Modeling a repeated measures growth curve

I have cumulative population totals data for the end of each month for two years (2016, 2017). I would like to combine these two years and treat each months cumulative total as a repeated measure (one ...
3
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1answer
93 views

Choosing Prior for $\sigma^2$ in the Normal (Polynomial) Regression Model $Y_i | \mu, \sigma^2 \sim \mathcal{N}(\mu_i, \sigma^2)$

I have the polynomial regression model $Y_i | \mu, \sigma^2 \sim \mathcal{N}(\mu_i, \sigma^2), i = 1, \dots, n \ \text{independent}$ $\mu_i = \alpha + \beta_1 x_{i1} + \beta_2 x_{i2} + \beta_3 x^2_{...
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0answers
8 views

identify parameters from non linear non separable regression model

suppose I have a regression model $$y_i = f(x_i,e_i;\beta) $$ where $y_i,x_i$ are observed data and $e_i$ are error. $\beta$ is parameter of interest. Assuming that $f$ is smooth, yet not invertable. ...
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1answer
43 views

Prediction Interval for Mean of Predictions

This question is about creating a prediction interval for the mean of predictions from a regressor. Let's say I have arbitrary regression function (not necessarily parametric, could be random forest, ...
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1answer
41 views

A proper function for nonlinear regression with 3 predictors

There are three independent variables in my experimental work, namely flow rate (0.5 ≤ Q ≤ 9 where ΔQ = 0.5), particle size (a = {6, 10, 15}), and a geometric parameter (AR = {AR1, AR2, AR3, AR4}). ...
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1answer
206 views

What is the essential difference between a neural network and nonlinear regression?

Artificial neural networks are often (demeneangly) called "glorified regressions". The main difference between ANNs and multiple / multivariate linear regression is of course, that the ANN models ...
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0answers
22 views

Can you fit a non-parametric regression such that the first derivative will be equal to zero for some specific points?

Given two variables x and y, where y=f(x)+error, is it possible to estimate a non-parametric regression of y on x taking into account the fact that we know that f(x) should take maximum or minimum for ...
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0answers
52 views

Nonlinear regression: improving parameter estimates

I'm running a nonlinear regression to estimate $\delta$ and $\alpha$ using the following model, where $X$, $Y$ and $Z$ are the variables: \begin{equation} Z = \left(\delta X^\alpha+(1-\delta)Y^\alpha\...
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0answers
27 views

Linear mixed model with three groups, alternative non-linear approachin R?

first thank you for your help. I'm quite new to to R, but specially in mixed models. Shortly i have three experimental settings from 31 subjects, i.e 3 repeated measurements from same subjects ( also ...
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0answers
46 views

How can local linear regression results be used in prediction?

I am building a nonlinear time series model, i.e., $$ y_t=f_1(y_{t-1})y_{t-1} + f_2(y_{t-1})y_{t-2} $$ for some mechanical vibrations. Many papers use local linear regression to describe the $f_1$ ...
2
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1answer
51 views

Variable Transformation to find Regression Parameters

I want to solve a nonlinear regression model $y=\alpha*\exp(\beta𝑥)$ using a linear regression model through variable transformation. Simple question up-front: Can I use log transformation even ...
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0answers
40 views

Interpretation of LOESS summary

I am using loess function in R for local regression. I am looking for an interpretation of summary of loess fit. Could someone ...
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0answers
40 views

Measure of relationship between two variables that are percentages containing many zeros

I am working with various different data sets (in the context of forest reclamation on industrial disturbed landscapes) that contain percent cover values of desired (planted) and undesired plant ...
0
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0answers
62 views

How to get the error associated with constant obtained from non linear regression of biological data?

I have a set of experimental data, where for each concentration of a protein my device generates a response. Obviously, for more concentration it generates greater response and thus the concentration (...
0
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0answers
136 views

Backward elimination for a non-linear multivariate regression

I'm trying to determine what would be a good model for my problem. I am not a statistician and use some words colloquially - please excuse my lack of knowledge. I'll illustrate the problem with the <...
0
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1answer
28 views

How to compute a non linear mix model with links between the parameters and their variance in R?

I'm working on a biological problem where we want to modelize the impact of a treatment and a chemical modification on the measured quantity of a molecule (peptides). We will note $x_{ijk}$ the ...
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0answers
46 views

Fitting a nonlinear model with a binary outcome

I have a binary outcome that I need to explain with an unusual non-linear function. I need to describe a binary outcomes as the sum of two 4-parameter logistic functions (with a = 0 for domain ...
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0answers
35 views

Order of entry of parameter bounds in lme4 [closed]

I have what, I think, is a very simple question. In nlmer from lme4 in R, the upper and lower bounds for parameters can be ...
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0answers
21 views

Non-Linear Regression

To start, excuse any terminology mistakes I make or the like. I have a set of data that has two parameters and a third expected outcome. ...
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0answers
29 views

Deriving bias from misspecified functional form

I am trying to derive the bias from omitting a quadratic term if the true model is indeed quadratic. For example, suppose I estimate: $y_t = b_0 + b_1x_t + e_t$ But the true model is: $y_t = b_0 + ...
1
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1answer
41 views

Adding nonlinear terms to multiple linear regression (MLR)

I just need a hint.(still learning) I'd like to create a simple model that uses MLR. Basically, I add some parameters (temperature, irradiation...) and predict a parameter. But I'd like to add also (...
1
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1answer
58 views

Outside of linear regression, what does it mean to say that the residuals should be independent?

I understand how to think about residuals in the context of linear regression: we have a dataset of N rows and columns x, y, of linear data $y = mx + \varepsilon$, we pick a linear model $f(x) = \hat ...
0
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1answer
20 views

Linear regresssion on body mass index

I am using a continuous variable of body mass index. I checked the distribution using statistical tests and determined it is not normally distributed. I think these results are driven by outliers, ...
0
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0answers
56 views

Estimating parameters from a non-linear model with uncertainties in both X and Y, plus multicollinearity

Summary: I'm interested in robustly estimating parameters and their uncertainties from a non-linear model given data, when the data have uncertainties in both the dependent and independent variables, ...
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2answers
45 views

Logistic Regression Models Without Main Effects?

I am building logistic regression models measuring human behaviour, which consist of categorical variables: demographics, conditions, and interactions between the demographics and the condition ...
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0answers
48 views

Explained variance in logistic regression based on regression coefficients

I am wondering about the relation between the explained variance and the regression coefficients in logistic regression. So given a multiple linear regression $y_i = \beta_0 + \sum_{k=1}^{K} \beta_k ...
1
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1answer
32 views

An application of AIC for non-linear models comparison

I am doing a comparison between two parametrical non-linear models with different amount of parameters. I am using Akaike information criterion (AIC) with the following formula: 2*k + N * log(RSS / N)...
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0answers
69 views

Comparing parameters of two nonlinear models

Suppose we use nonlinear regression (specifically the nls-package in R) for fitting separate models (e.g. same equation, different values of parameters) for two (or more for that matter) conditions in ...
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0answers
46 views

non-linear logistic regression

I have the non-linear logistic regression model $$ \text{logit}\Pr(Y=1|X_1,X_2,)=X_1X_2\frac{1}{m(2+\theta)TD_{50}}+X_1\frac{\theta }{m(2+\theta) TD_{50}}-\frac{1}{m} $$ which I will like to estimate ...
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0answers
18 views

Endogeneity in Recursive Probability Models

I am trying to estimate the causal effect of $\{\Psi_i\}_{i=1}^M$ on $Y$. Where $\Psi_i$ are probabilities, and there is simultaneity between $\Psi_i$ and $Y$. The proposed methodology is first to ...