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Questions tagged [nonlinear-regression]

Use this tag only for regression models in which the response is a nonlinear function of the parameters. Do not use this tag for nonlinear data transformation.

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Regression model using combination of ranges/parts

My main goal is making predictions using a nonlinear model that have many independent variables. I would like to split my numerical independent variables into ranges/parts. Then to use a combination ...
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I need help with choosing a mid-long term forecastic method for this demand

I am trying to forecast the demand of a product for the next 36 months, based on its sales history. The demand plot is shown below. I honestly don't know what to do with it. I tried linear and non-...
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How can I determine, in what extent the fit to experimental data is good in Matlab?

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
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1answer
29 views

Is it possible to calculate F-value for a neural network regression model?

I trained a model using neural network regression and used the F-value equation that is used for calculating F-value for linear regression: F=(SUM(Ypredicted-Ymean)^2/p)/(SUM(Ypredicted-Yobserved)^2/...
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Do we need ergodic-stationarity of the response variable in OLS spline regression?

I was wondering if we need the response variable to be ergodic stationarity when estimating an OLS spline regression. My intuition tells me that it's not needed but I would like to have a confirmation ...
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confidence limits on model parameters : Monte carlo vs chi-square

I performed a non-linear fitting on experimental datas to determine model parameters using least square methods ($\sigma$ is the same for all the experimental datas). And now, I want to determine ...
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1answer
35 views

Selecting appropriate likelihood during non-linear regression

When performing regression to fit a function, $f (x,{\bf \beta})$, to a set of observed data, $y_i(x_i)$, we are seeking to optimize the parameters, $\beta$, of the fitting function, to minimize some ...
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Should I standardize my variable for regression before nonlinear feature transformation?

I would like to fit a non-linear model by doing nonlinear feature transformation first (e.g. exp, log) and then using linear regression (or regularized linear regression). However, I am stuck at ...
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44 views

Linear regression feature selection equivalent for a classification problem?

I have the following: Label (y): a boolean flag indicating something is good or bad Features (X): lower-level features that are believed to be correlated with the boolean flag. Some of them are ...
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2answers
41 views

Would machine learning techniques help if the linear and nonlinear relationships is so weak?

I have a cross sectional data set at hand contains four predictors to predict one outcome, I employed bivariate analyses to check whether the relationship between the dependent and independent ...
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21 views

Is there a correlation coefficent for “smooth” functions?

There is Pearson's, which measures linear relationships. There is also Spearman's, which can detect monotonic relationships. I am wondering if there is a similar coefficient someone has come up with ...
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How to analyze a small dataset?

I have this dataset and I'm not sure how to analyze it. I threw the classical regression methods such as OLS at it and haven't achieved much success. My response variables are ...
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33 views

nonlinear regression with time series error

I have a question about data analysis. I fitted my data to non linear regression by using nls function in R. Then I plot the residuals. The residuals are non ...
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35 views

GAM residuals , GAM check

I am doing my GAM regression analysis in R and by using the gam.check() function from the ...
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1answer
54 views

Linear Model (on X or in $\beta$?)

I'm well aware that when we use the expression "linear model" we are actually making reference to models that are linear on the parameters $\beta$. And because of that any polynomial regression will ...
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2answers
54 views

Neural networks for regression vs. more classical regression methods?

I am interested in learning about when one would use neural networks for a regression problem over a more classical regression method such as least squares. Is it mostly related to the complexity of ...
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21 views

Are there any good, general optimization algorithms for nonlinear regression in R?

I have generated data similar to a model I want to build: ...
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214 views

How can I test if the two parameter estimates in the same model are significantly different?

I have the model $$ y=x^a \times z^b + e $$ where $y$ is the dependent variable, $x$ and $z$ are explanatory variables, $a$ and $b$ are the parameters and $e$ is an error term. I have parameter ...
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How to estimate error of regression parameters from data with errors

I'm a physics student and in school we often measure some data (like voltage and current) and then use regression to determine an unknown quantity (ie. resistance in this case). My problem is that I ...
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21 views

Set different link functions in Generalized Mixed Effects Model in R

Suppose I have a dataset of fish, some are salmon some are trout. I have a bivariate regression model specified roughly like below: prob(caught) = 0.5 + 0.5 * logit_inv(diet + fish_type) for salmon ...
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63 views

Using UMAP or other non-linear dimension reduction techniques on response variables prior to learning?

Background Suppose you have a training set where the response measurements are some $N$-dimensional vectors of related measurements - in my specific case, they happen to be cell viability scores for ...
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1answer
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What is the purpose of doing a logistic regression when the predictor is dichotomous?

I would like to expand on this question. Knowing that it is possible to do a logistic regression when the IV is dichotomous, and that I've seen it done in studies: what is the purpose of doing so, and ...
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1answer
105 views

Non-linear regression with vectors as observations [closed]

I'm blocking on a computational problem, that is fitting a function $\begin{array}{lrcl} f_{\alpha} : & \mathbb{R}^k & \longrightarrow & \mathbb{R} \end{array}$ to observations $(x_1, ...,...
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Regression of the difference between 2 poulations in the same variable and a third variable

I want to perform a simple linear regression. I have the color indices of red flower and blue flower (E.g. red could have a number between 5 to 50 of how red it is, and blue, on the same scale, of how ...
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1answer
68 views

Check if log-likelihood function is correctly derived

This question is a continuation of this one. By guesswork, I found out that $\vec{\theta}=(5.2,5.3,1.0)=$ $(A,B,C)$ was a good guess that made my model $$y_i=A\sin\left(\frac{x_i}{B}\right)+C\...
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Discrete-time survival model as linear probability model

Discrete-time survival (event history) models are typically estimated using a nonlinear transformation such as logit, probit, or completementary log-log. Logit assumes proportional odds, and similarly ...
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2answers
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How to guess starting value for non-linear regression

I used proc nlmixed in SAS to calculate the beta estimates in non-linear regression model, while I'm not sure how to guess the starting values of the parameters. By ...
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1answer
37 views

Fitting a NN model on one-to-many function

Given $f(x) = y$ as a surjective (many-to-one) function, we know that $f^{-1} (y) = x$ is a one-to-many mapping for function $f^{-1}$. In my application, $x$ is a spatial data represented by a 2D ...
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Adaptive knot selection for B-spline fitting

When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve ...
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Non-linear regression. Obtain B.spline coefficients using Fourier Transform?

I came up with a idea to estimate the coefficients of a B-spline fit by using the Fourier Transform but I don't know if it makes any sense to estimate them in this way. Given that $$s(x)=\sum_kc(k)\...
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0answers
30 views

How to understand the results of nonlinear mixed-effects regression model

I have some data, obtained from 4 different groups. Each repeat is some 4 parametric sigmoid. I need to fit the data to sigmoidal function and answer the question, whether sigmoids are different ...
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1answer
59 views

CUSUM test for a Nonlinear Regression Model

I would like to do a CUSUM test for the regression parameters of a nonlinear regression model to analyze possible parameters variations. For linear regression models the CUSUM test is based on the ...
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1answer
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Calculating prediction bounds from composite data

I have several (partially overlapping) data curves of oscilloscope-measured detector voltage as a function of time (very simple hypothetical example as follows): There is an underlying physics ...
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2answers
44 views

Slope of Curve with Unknown Functional Form

I have a monotonically-increasing curve whose functional form is not known a priori and would like to compute the curve's slope at the rightmost endpoint. Typically, when the functional form is known, ...
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1answer
62 views

Curve fitting in the presence of prior beliefs about the relationship between x and y

In the figure which follows each dot represents a game of a particular sport. The x-axis represents the home team's margin of victory, and so around the top-right we can see a game where a home team ...
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Is a Logistic Regression always viable for having a dichotomous response variable?

I have learned some about a simple logistic regression with one explanatory variable (quantitative) and one response variable (binary: $0$ or $1$) Generally the plot for such a set of data may look ...
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2answers
203 views

Difference between Gaussian process regression and other regression techniques (say linear regression)

I am confused about the differences in the regression techniques available. Take for example, linear regression. In this case, we construct a model $y = \beta^Tx + \epsilon$ where $\epsilon \sim N(0,\...
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1answer
117 views

Neural networks to predict a nonlinear curve

I want to model a complex nonlinear function using neural networks (keras). Training data: input - 8500 x 176 matrix of features, output - 8500 x 8 matrix, each row corresponds to 8 points which ...
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0answers
41 views

Fitting a logistic growth curve with an iterative formula in R

I'm trying to fit a logistic growth curve to specific countries GDP data using an equation, $P_{n+1} = rP_n(1-\frac {P_n}{k})$. (1) I've found constants $r$ and $k$ simply by finding a ...
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1answer
60 views

Kernel ridge regression with matrix-vector data set $S := \{ X_i, y_i \}_{i=1}^{N}$?

Please notice that this question was asked in MO, but it seems that it doesn't interest MO community. So, I have got a comment to post in this community in the hope that I may get some attention to ...
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3answers
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Name of logistic regression with two dependent variables?

my understanding is that Multinomial logistic regression is where your dependent variable could take values of 1,2 or 3 where 1-3 are classes. But what isit called if you have two dependent variables ...
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1answer
28 views

Systematic way to determine if a model is linear or nonlinear? [duplicate]

Determine whether the following models are linear, intrinsically linear, or nonlinear (disregard the error structure): $y=\beta_0+\beta_1 x_1 +\beta_2 x_2^{\beta_3}+\epsilon$ $y=\beta_1 + \...
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1answer
138 views

Estimating the Parameters for $y=\beta_1 e^{\beta_2 x}+\beta_3 z+\epsilon$

I have the model $$y=\beta_1 e^{\beta_2 x}+\beta_3 z+\epsilon$$ where $z$ is an indicator variable. I need to obtain estimates from linear regression to get initial values for the parameters. Then I ...
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1answer
42 views

How do I find an appropriate test statistic for the derivative of a quadratic regression curve?

Suppose I've managed to fit a quadratic regression curve $Y=\beta_0+\beta_1X+\beta_2X^2$ to a dataset. Given some $X=x$, I'm looking for an appropriate test statistic to check if $x$ is an extreme ...
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31 views

Piecewise integration

I am trying to estimate residential demand for electricity in a country where electricity is sold (to all households (HH)) at an increasing two-part tariff. By choosing marginal prices as my key ...
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1answer
54 views

regression - does R2 only apply to measure linear regression performance?

Background According to Wiki: https://en.wikipedia.org/wiki/Coefficient_of_determination, $R^2$ is coefficient of determinant. The definition is $$ R^2 = 1 - \dfrac{SSE}{SST} $$ Since $SSE$ is ...
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Which test to use to detect difference in proportion between more than 2 groups? Logistic regression?

I have data that looks like this: there is a group of 27 subjects with one dichotomous variable y1 at 3 times points. The propbability of y1 is different between the 3 time points (100%, 85%, and 40% ...
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2answers
124 views

What do neural networks offer that traditional non-linear statistical models do not offer?

I have tried to find an answer to this question but have not found a satisfactory answer. I understand that neural networks(NNs) offer the potential to complex build non-linear models. What I don’t ...
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Relevance of residual normally distributed residuals in nonlinear regression

I have a mathematical equation, based on physics, that requires estimating several parameters via nonlinear regression. I have conducted such nonlinear regression estimation with a dataset of 1100 ...