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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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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
21 views

Calculate the predicted model accuracy in python for regression problem [on hold]

I want to calculate my model accuracy for rainfall forecasting. I already calculated MAE, RMSE, MAPE for rainfall forecasting. But want to know the total model accuracy, for instance, my model is ...
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1answer
26 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
17 views

Models under Regression Analysis list [on hold]

I am compiling a list of models under Regression analysis(Whatever I think is useful for Machine learning) which is divided into two models i.e Parametric and Non-parametric Regression. Got most of ...
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0answers
23 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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0answers
9 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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0answers
33 views

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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3answers
26 views

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
23 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
126 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 ...
3
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1answer
32 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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26 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 ...
4
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1answer
44 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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0answers
25 views

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
102 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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0answers
24 views

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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0answers
11 views

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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1answer
38 views

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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1answer
81 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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0answers
18 views

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) ...
2
votes
1answer
78 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
14 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
30 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
61 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
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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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
96 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
51 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
53 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 ...
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2answers
98 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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0answers
27 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{\...
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0answers
122 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
18 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
248 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
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1answer
44 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
12 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
232 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
9 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
57 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
47 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
438 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
23 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
54 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
30 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
48 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
94 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 ...