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Questions tagged [nonlinear-regression]

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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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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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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Non-linear regression with vectors as observations [on hold]

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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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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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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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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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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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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Selection of regression model for prediction and interpreting quadratic regression results

I am regressing between the body mass and eye diameter in different bat species. The relationship is non-linear (picture attached) as the eye-size cannot increase linearly with respect to body size ...
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Fitting quadratic model for non-normal data

I am regressing between the body size and eye size values of different bat species. They are not linearly related (picture attached) and I want to fit a quadratic model to it but the values are non-...
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Fitting polynomial equation and combined effect

I have following type of data matrix. I want to find the significance of predictor (including combined effect) variables like, y=β_0+β_1 x_1+β_2 x_2+β_3 x_3+β_4 x_1^2+β_4 x_1^2+β_5 x_2^2+β_6 x_3^2+...
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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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Fitting data on a time demanding stochastic Model

I have a multi-parameter (8 at least) model which is very time consuming. It's not an analytical function but instead is a model which integrates many differential equation and some times the result ...
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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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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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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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42 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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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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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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Estimating a regression equation with a hill function transformed independent variables

I'm currently trying to estimate the following equation: $$y = \text{const} + \beta \frac{x^\gamma}{x^\gamma+\rho^\gamma}$$ So, I have to estimate 3 parameters for every variable plus a constant. A ...
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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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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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132 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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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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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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51 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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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 ...
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Consistency of quasi MLE of nonlinear model

I am working on a project involves the quasi MLE for nonlinear model. Suppose the model is given by $w^Ty_t=w^TX_t \beta+w^Tu_t$ for $t=1,..,T$ subject to $w^Tw=1$, where $w$ is a $k_1 \times 1$ ...
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Feedforward Neural networks for Regression confusion

I’m a bit confused about the concept of using feedforwrd neural networks via backpropagation to model a nonlinear relationship between the input and output variable in a regression setting. Can this ...
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131 views

Understanding Maximum Likelihood Estimation (MLE) and its confidence intervals

I'm trying to figure out if I am actually understanding MLE correctly, or at least applying it correctly to my data. My data consists of several patients for which I have some data, which is used in ...
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Finding when an external effect appears in time series using regression analysis

I have the 'seen' data (post views, PV) of different social media channels over a period of time and I want to see whether the effect of an external factor (EF, for instance, internet accessibility) ...
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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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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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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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32 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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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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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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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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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. ...
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Non-Linear Fit Preserving Normalisation

I have a problem I have been struggling with for a while: I need to carry out a non-linear fit (and this is the easy part). I have a set of discrete values {x1,x2...xN} and the corresponding {y1, y2......
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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 ...
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178 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 ...
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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{\...