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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What do I do with zero columns in a tensor.prod.model.matrix?

Suppose my two marginal bases are given by (for variable $p$ and $t$ the degree is equal to $1$ and $5$ inner knots are used). ...
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21 views

Comparing nested, non-linear models

I would like to compare the fit of two non-linear regression models: 1) $$ Y = (\Pi^{10}_{i=1}\beta_i^{x_i})^{1/\Sigma \beta} $$ 2) $$ Y = \begin{cases} (\Pi^{10}_{i=1}\alpha_i ...
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1answer
44 views

Regresssion of Accurate Data

I'm collecting calibration data for a device which involves three variables $S$, $L$, and $x$. For a given coordinate $(S, L)$, the device will provide me with the corresponding value of $x$ to a high ...
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10 views

Multiclass logistic regression update algorithm

http://web.engr.oregonstate.edu/~xfern/classes/cs534/notes/logistic-regression-note.pdf See section 2 called Multi-class Logistic regression, especially the update rules. (The entire section is only ...
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127 views

Selection of k knots in regression smoothing spline equivalent to k categorical variables?

I'm working on a predictive cost model where the patient's age (an integer quantity measured in years) is one of the predictor variables. A strong nonlinear relationship between age and risk of a ...
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21 views

Problems with curve fitting

I have a longitudinal dataset to which I am trying to fit the following model : $$ y_{i,j} = \frac{1}{1+a_{i} \exp(-r_{i}t_{i,j})} + \varepsilon_{i,j} \tag{1}$$ The setting : $i$ ($1 \leq i \leq ...
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18 views

How to calculate standard errors of a non-linear model prediction?

I'm trying to understand how to show the prediction error of a model fit in R using the non-linear least squares function nls. Although there is an argument ...
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4answers
54 views

Beta confidence intervals in transformed linear regression

Let's say I have a model: $$Y_i = \beta_0 \beta_1^{X_i} \epsilon_i$$ (note: This is slightly different than the more common example case of $Y_i = \alpha e^{\beta x_i}\epsilon_i$.) I can take the ...
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18 views

Nonlinear Random Effects Model Specification in R

I have a dependent variable w with independent variable x representing time, which is clustered by variable site. In addition, I have indicator variables for 3 time period: i1, i2, i3, which ...
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14 views

Modify Levenberg Marquardt

Could you kindly let me know if it is possible to print parameters to the console as they are being optimized (using the levenberg marquardt algorithm) in python/matlab? I have been trying to do so ...
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1answer
91 views

How to calculate 95% confidence interval for non-linear equation?

I have an equation to predict the weight of manatees from their age, in days (dias, in portuguese): R <- function(a, b, c, dias) c + a*(1 - exp(-b*dias)) I ...
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18 views

Statistics for catch of tuna longline

I have study on catch for tuna longline. In here I have 3 independent variables (number of hooks, length of branch line & baits) and 3 dependent variables (catch of tuna, catch of marlin & ...
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1answer
32 views

How do I prove the significance of a non-linear model?

For example, for linear models, you take the p-value of the regression, and you deduce if the regression is or not significative. But with non linear models, in R, there isn't shown a p-value ...
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3answers
357 views

Why is polynomial regression considered a special case of multiple linear regression?

If polynomial regression models nonlinear relationships, how can it be considered a special case of multiple linear regression? Wikipedia notes that "Although polynomial regression fits a nonlinear ...
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1answer
59 views

Interaction effects in non-linear models

I have a general question about interpreting interaction effects in a non-linear model. I understand the reasons Ai and Norton (2004) suggest using the stata inteff command to help interpret ...
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1answer
60 views

Comparing two curves with different x-axis points - appropriate test?

I have two curves and I want to be able to calculate the probability of these curves coming from different distributions or another appropriate statistic. Each curve is fitted through the mean of ...
2
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1answer
77 views

How to solve the problem, that the scale of variables influence the gradient/optimization

I've the problem that, using something related to Fisher-scoring, the gradient, which is usually the sum over a variable times a value which depends upon the parameter we are looking for, the updates ...
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1answer
51 views

Type of regression method to use

I have the marker data of 32 patients for eight different markers. WHat needs to be done here is to predict the type of marker which is suitable for the disease control. I used Disease control as the ...
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27 views

Is it possible to estimate the convex combination of parameters in the IRLS-Framework?

Suppose I want to estimate the parameter $\mathbb{E}(Y)=\mu \ge 0$ with $\mu = a(\alpha)\mu_1(\gamma_1) + \Big(1-a(\alpha)\Big)\mu_2(\gamma_2)$ where $a(\alpha)\in (0,1)$ Using the usual ...
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1answer
84 views

What is SVM regression? Is it for regression or classification?

I'm trying to understand what is SVM regression. It's used for classification or regression? Can someone give an intuitive understanding of it?
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26 views

How to deal with imperfect multicollinearity

I am estimating a model for an assignment, and found out that there is a 0.9 correlation between two of the independent variables. So If I am not wrong I should omit one variable and redo the ...
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1answer
20 views

Neural Networks output range in simulation

I am learning some model based on examples ${((x_{i1},x_{i2},....,x_{ip}),y_i)}_{i=1...N}$ using a neural network of Feed Forward Multilayer Perceptron (newff) (using python library neurolab). I ...
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24 views

Regression clustering

I am looking for references about classical methods in regression clustering. My problem is the following: I have a cloud of points that are assumed to have been generated by inverse functions with ...
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0answers
24 views

Model selection for nonlinear regression of a Gaussian CDF mixture distribution

I have a number of distributions which I want to fit to a CDF that is comprised of one or more Gaussian CDFs. I was able to use weighted least squares regression to find the best fit parameters for ...
2
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0answers
79 views

Linearity Assumption in OLS with Dummy Variables

Dumb question but let's say that I have a continuous response variable and have constructed a regression model with multiple predictors. Most of my predictors are continuous but I have one which is a ...
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34 views

Volume contribution decomposition in Log-log models

I am currently working on pricing analysis : the effect of competitor SKU pricing on the number of units sold of my SKU. The model was built on the log(units) sold. I want to measure the contribution ...
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2answers
145 views

Marginal effect of squared variable in Probit Model

I want to estimate the following probit model $employed_t=\beta_1 age + \beta_2 age^2$ and I use the Stata code probit employed c.age##c.age Using the command ...
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35 views

Implement neural network to perform multivariate poisson regression with implied rates

I am now looking at implementing a neural network that will take in 4 input variables, and will output 24 variables. All of the output variables are related (in more than one way) to each other so I ...
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1answer
27 views

data prediction by regression or better ways

I am working on data prediction. Given data of a random variable $X$ and $Y$, find out how to predict $Y$ from $X$. I know how to do it by linear regression, $\hat{Y} = kX + b$. But, here, $X$ is ...
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1answer
50 views

Specific type of dummy regression

I would like to regress the values on the y-axis by the values of the x-axis. As you can see, the relationship is not linear. Values of y are only positive can not exceed 4, values of x are always ...
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1answer
125 views

Linear statistical model with two-class variables

Suppose I have a set of (discrete) variables, say $X_1,\dots,X_n$. Each $i$ belongs to either class A or class B. When it belongs to A the contribution is $Y_{A,i}f(X_i)$, and when it belongs to B the ...
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37 views

using outcome of clustering as an ordinal scale for regression - feasible?

Suppose I have access to five dental surgeries, who volunteered to collect data about patients and their regular check-ups. The dental surgeries are quite up to completely different from each other ...
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54 views

Correction for non-linear trend seen in residuals plot when predictor is categorical

I'm running a linear regression analysis in R. One variable is a continuous outcome variable (score2) and the other is a categorical variable for treatment group ...
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54 views

Maximum likelihood estimation for custom equation in R

For this non-linear equation $$y = a\left(1-\exp\left(-\left(x/b\right)\right)\right)^c$$ by using least square estimated values for the parameters are obtained and ...
2
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1answer
202 views

Calculate log-likelihood “by hand” for generalized nonlinear least squares regression (nlme)

I'm trying to calculate the log-likelihood for a generalized nonlinear least squares regression for the function $f(x)=\frac{\beta_1}{(1+\frac x\beta_2)^{\beta_3}}$ optimized by the ...
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0answers
20 views

Measurement error in nonlinear models, when can one ignore it? and what can one do about it?

Suppose you know there is measurement error in your system but you don't have any idea what the variance is. In my specific case I have a nonlinear model \begin{align} y_i&=\epsilon_i ...
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2answers
155 views

Shape of confidence and prediction intervals for nonlinear regression

Are the confidence and prediction bands around a non-linear regression supposed to be symmetrical around the regression line? Meaning they do not take on the hour-glass shape as in the case of the ...
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25 views

Estimating confidence of a prediction

Given a set of features vectors $X=\{\vec{x}_1,..,\vec{x}_n\}$, binary ground truth data $Y=\{y_1,..,y_n\}$ and continuous prediction $\bar{Y} = \{\bar{y}_1,..,\bar{y}_n\}\in [0,1]$, I want to perform ...
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1answer
65 views

How to incorporate constraints in random forest output

Suppose I am doing random forest classification of labels $A$,$B$,$C$,$D$. There is some theoretical ordering to this output such that when $A$ is more likely than $B$, $B$ is also more likely than ...
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38 views

Nonparametric regression with restrictions

I need to estimate the function $f$ in the following object $$E[Y|X=x] = a(x)f(x) + b(x)f'(x)$$ with $a(x),b(x)$ known. What would be the optimal strategy to do this? I tried to do the cubic spline ...
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43 views

Where to start with nonlinear regression?

What are some good introductory materials for learning non-linear regression modeling? Bonus points for anything freely available. Thanks!
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26 views

Correlation and colinearity in nonlinear regression?

i have a new data set which is basically as bad as the last (same sort of data) and have been asked to try non linear regression on it, with the focus on partition (I will be using boosting and ...
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39 views

How can I evaluate my nonlinear model (without a model comparison)?

I have a non-linear model that seems to work quite well. Compared to other similar models, using the same data it has significantly more negative AIC and BIC, so I'm quite confident that it is better ...
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11 views

How to deal with heteroscedasticity in nonlinear system of equations?

What is the best way of dealing with unknown form of heteroscedasticity in nonlinear system of equations? Thanks in advance.
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36 views

Non Linear Rolling Regression

I'm trying to do rolling regression for the nonlinear equation (exponential). My functional form (stata form) for nonlinear equation is: ...
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51 views

Logistic Regression - Model Selection Method [duplicate]

What is the best way to know the best selection method for our logistic regression model ? Forward Selection Backward Elimination Step-wise Selection Full Model. I am running logistic regression ...
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35 views

Confirming multicollinearity with small number predictors (after initial model construction)

I am working on a dataset with with 100 or so X variables and the effects on a single Y. As with previous threads this contains a lot of fairly significant correlations. I considered using PCA but ...
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96 views

Parameters of $ y_i = \beta_0^2 + \beta_0 \beta_1 x_i$

I have this model, nonlinear in the parameters $ y = \beta_0^2 + \beta_0 \beta_1 x_i $ exist a known estimation of parameters ?
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37 views

How do we know that a classifier is linear or not?

I searched on the net, but I could not find any really good answer to my question which is very easy. A linear classifier is a classifier which can classify the samples correctly. But Given a ...
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66 views

Use nonlinear mixed model for binomial distributed data

I frequently use this model to test catch efficiency and size selection properties of a given trawl fishing gear: \begin{equation} \theta(l)=\frac{s\times r(l)}{(1-s)+s\times r(l)} \end{equation} ...