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*).

learn more… | top users | synonyms

0
votes
0answers
15 views
+50

Estimating data set size for pattern extraction

I have a dependency treebank comprised of 100 structures, which is divided into a training set and a test set. I extract some rules ((DS,PS) pairs) to convert the treebank to phrase structures. When I ...
5
votes
0answers
34 views

Can we use bootstrap samples that are smaller than original sample?

I want to use bootstrapping to estimate confidence intervals for estimated parameters from a panel dataset with N=250 firms and T=50 month. The estimation of parameters is computationally expensive (...
3
votes
1answer
38 views

Good text on nonlinear regression (M.S. graduate-level)?

I've covered a linear models sequence where the classes discussed linear models using matrices, covering various experimental designs (split-plot, for example), ANOVA using matrices, and ending with ...
3
votes
1answer
245 views

Regression when response variable is a function

I have a set of data $(X_i,Y_i)$, $i=1,\ldots,n$ where $X$ and $Y$ are supposed to satisfy the following equation $$ y = \beta_0(1+x^2)^{\beta_1},\quad x>0, \quad\quad (1) $$ I am interested in ...
1
vote
0answers
31 views

Non-convergence in nonlinear regression

I've been studying a manuscript from the chemistry literature (not mine) that resorted to a trick to obtain convergence of a non-linear model fitted to experimental data. They wanted to estimate a ...
1
vote
0answers
23 views

Non-linear least squares and the distribution of an estimator

I have been trying to find the asymptotic normality of the non-linear least squares estimator. If I start with $0=X_t(\beta)'(y_t-x_t(\beta))$. I know that I have to perform Taylor expansion around ...
1
vote
0answers
12 views

Estimating covariance matrix from multiple distance measurements

I have a setup that can measure the distance between two beacons. The first beacon is aware of its 2D location and is moving around while measuring the distance to the second beacon. I've setup a ...
1
vote
0answers
30 views

Circular regression- R-Squared Value

Just like we have $R^2$ in linear regression, How do I find out the 'goodness of fit' of a circle to a given data? Is it wrong to use the $R^2$ formula from linear regression, $R^2 \equiv 1 - \frac{...
3
votes
2answers
102 views

suitable non-linear equation to capture a 'J-shaped' relationship between x and y

I am trying to model the relationship between forest age and individual tree mortality rate. The probability of mortality declines rapidly as forests go from being very young, and then creeps back up ...
1
vote
1answer
58 views

Fitting a nonlinear regression $Y=1 - a^{-bx}$

I have the following dataset: where X:Y 1:0.81 2:0.86 4:0.9 6:0.93 8:0.96 10:0.98 12:0.99 14:0.99 16:1 18:1 20:1 ..:1 Since the limit of the regression ...
0
votes
0answers
16 views

Validating regression - common and best practice

Is there a reference setting out a best practice way to validate a regression (such as Lasso, but in general any automated regression), and what is done in practice? My motivation for the question is ...
1
vote
0answers
16 views

How to relate distributions?

I have 100 objects. Each object has 10 (highly correlated) attributes that I can measure. For each object, I obtain 10000 samples of that object's attributes. I now want to relate the attributes ...
0
votes
0answers
10 views

Why doesn't the logistic regression model include error? [duplicate]

I know it comes from the fact that y is a vector that only has binary values, but I'm looking for a better explanation...
0
votes
1answer
39 views

What the interpretation when both the non-squared and squared term are significant?

I have a logistic regression model and added for a curvelinear effect both the non squared term and a squared term to the regression model. They are however, both significant. How do i interpret this?
0
votes
2answers
39 views

Help interpreting interaction terms in proportional cumulative logistic regression- ordinal regression

I am using the polr() function in R to analyze the relationship between a students score on their first exam, their score in their prerequisite course, and their beginning of semester GPA on their ...
2
votes
0answers
31 views

Which non-parametric multiple-regression methods are computationally efficient with respect to the number of regressors?

I did some regression in R with random forests and got some decent results, $1-\sum{|e_i|}/\sum{|y_i-\bar{y}|}=0.692$, but I want to do better than this. Through my research, I have concluded that the ...
0
votes
2answers
49 views

How to interpret Quadratic Terms

I'm answering a practice exam questions, and having trouble with one on quadratic terms. Could someone give me a quick summery of 1) why they are sometimes included? 2) How to interpret them? In ...
1
vote
1answer
38 views

Non-linear function optimisation using nlminb function in R

I have been getting error messages in my attempt to estimate parameters in a non-linear function using nlminb function. The following is the code: ...
0
votes
1answer
36 views

Can nonlinear regression with least squares estimations be used for testing hypotheses with data containing dependent observations?

I counted the number of animals of a certain species in 6 fixed locations on a monthly basis for 18 months. I now would like to test the effects of location, starting density, and time on the dynamics ...
0
votes
0answers
12 views

dependent variable in shares, independent variable log transformed

I havea question. My dependent variable is in percentage (shares of renewables in total energy supply). Hence, my variable is bounded but values are not closed to the bounds. My professor told me that ...
0
votes
0answers
33 views

Nonlinear regression vs. GLMs for estimating ED50

Are binomial GLMs better than nonlinear regression for model-fitting, and predicting ED50s and other effective dose point intercepts? In toxicology it is typical to run an experiment with a ...
1
vote
0answers
28 views

Significance testing between two hyperbolic curves

I have two curves for biological data (one-site binding). These curves were both fit using the following (Michaelis-Menten) model: BRET2 = (Bmax * RFU_RLU)/(Kd + RFU_RLU) Note: (x,y) here is ...
0
votes
0answers
11 views

How to assign defined training set, val set and test set for training a Neural net in NNtoolbox?

To find an optimal number of hidden neurons and layers in my code using feedforward net, I use cross validation technique and cvpartition function to split data. Now my aim is to use this split data ...
7
votes
2answers
81 views

Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$?

If I have theoretical reasons to suppose the data might be fit with an unusual equation such as the following: $$Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$$ Can I use ...
1
vote
1answer
35 views

How do you do a non-linear Poisson? What even is it?

I have a count data that I am having trouble transforming to be linear. First, what are smoothing functions and how do I do it in R? Let's use the famous crab satellite example. If you plot width to ...
0
votes
0answers
10 views

How are the values of knots in MARS calculated?

I'm wondering how the MARS algorithm decides on the specific values for the knots which are included in the hinge functions. Thank you very much.
0
votes
0answers
4 views

bilinear regression (or broken power law) and non-detections (upper limits)

I am trying to figure out what is the best way to fit a set of two-dimensional data (x and y, presumably independent) with two segments of linear models and a ``break point''? The tricky part of the ...
0
votes
0answers
6 views

what do the outputs of usl model mean?

I am trying to understand the summary of the universal scalibility law model: ...
1
vote
0answers
18 views

One-Step estimators for non-linear regression

'Disclosure': This question is also asked in the economics.stack community, under the tag of Econometrics, with same title. I'm not sure if it's too technical for that community. Let's suppose I ...
0
votes
0answers
12 views

Is there a p-value(or standard error) interpretation in a non parametric approach?

In a parametric world , we always report p-value or standard error in a parathesis below some coefficient from a regression , which is a significance testing. How about in a parametric world? I guess ...
1
vote
0answers
19 views

Regression of outcome variable with sinusoidal periodicity?

In linear regression of an outcome variable with sinusoidal periodicity (eg seasonal temperature variation), is it sufficient to adjust for this variation by adding a cosine function [1] as a ...
2
votes
1answer
25 views

Non-Linear Relationship for a Log-Log Model

I currently have a log-log model. Its scatter plot looks like this: I am currently stuck after this. I need to find a non-linear relationship to predict how log (X Variable) will affect log (Y ...
0
votes
0answers
14 views

Nonlinear permutation tests

I'd like to carry out additional tests on the estimated model parameters from a nonlinear model. The goals and methods are nicely presented in the 'predictmeans' package in R for linear models. Does ...
1
vote
1answer
31 views

Control Function (CF) Approach with Nonlinear Functions of Endogenous Variables

I am estimating a model using the control function approach (also "2SRI"). My model includes an endogenous variable $y_2$, an instrument $z_2$ and an interaction of $y_2$ with an exogenous variable $...
1
vote
1answer
44 views

Mixing exponential and linear regression with multiple predictors

This is the data set I am working on, trying to predict count (last column) : ...
3
votes
1answer
53 views

How does one prove asymptotic normality of the Non-linear least squares from First order conditions?

Our model is $Y=X(\beta_0)+u$, where $u\sim IID(0,\sigma_0^2I)$, and $X(\beta)$ is a non-linear function of the beta. When trying to minimize the $SSR(\beta)$ we get the following FOC: $\nabla X(\...
1
vote
0answers
30 views

Non-Linear Regression on model with time delay (dirac function)

here is the equation: $$y(t) = K_{2}\delta(t-\theta ) \Bigg(1-\frac{\tau_{1}e^{\frac{-(t-\theta)}{\tau_{1}}}-\tau_{2}e^{\frac{-(t-\theta)}{\tau_{2}}}}{\tau_{1}-\tau_{2}}\Bigg)$$ The parameters that ...
0
votes
1answer
64 views

How to make a model for the given data in sas?

I have a nonlinear model: $$r10^{\beta_0-\beta_1A-\beta_2B-\beta_4D-\beta_{2,4}BD} $$. I used sas to test different models. Here is the code: ...
1
vote
0answers
18 views

Exact Solution for a Nonlinear Least Squares Problem

For any linear least squares problem, we know that a unique solution always exists and that it can be explicitly written down in a closed form. My questions is that, is there any example of a ...
0
votes
1answer
79 views

How to use final svm regression model to predict new values of the dataset

I understand svm_predict function can be used to estimate or predict test output, but the arguments passed are like this svm_estimate = svmpredict(y, X, model); ...
1
vote
1answer
30 views

How to use a sigmoidal function in a multiple (non)linear regression

My data follows a sigmoidal function of the form $$y=asym/(1+e^{(xmid-x)/scale)})$$ I have taken the function from the SSLogis function in R. My supervisor and I think that there is a second variable ...
1
vote
2answers
44 views

Fitting nonlinear curves and getting parameters

I have the following data $(s_i, t_i)$: $s_i:$ -337.6 202.1 341 387 397.2 $t_i:$ 0.1 1.28 2.418 3.54 4.628 And also have the equation: $s_i= x - y*\exp(-t_i/z)$ How can I get those 3 ...
1
vote
0answers
51 views

Non-linear least squares standard error calculation in R

I am using implementations of the Levenberg-Marquardt algorithm for non-linear least squares regression based on MINPACK-1 utilizing either the R function nlsLM() from minpack.lm or an implementation ...
1
vote
0answers
33 views

when fitting non-linear data set to linear model

What is the residual standard deviation? Can I see whether the model I used is accurate or not by looking at this measure? In fact, I try to understand whether my data set is fitting to linear ...
1
vote
2answers
50 views

What is an intuitive explanation for the interaction of factors in a multiple regression?

How should one proceed when the interaction of predictors in a multiple linear regression is significant? I'm really after an "explain like I'm 5" type of explanation. Even better if it's supported ...
1
vote
1answer
51 views

Statstical test for the best algorithm for regression cross-validation

I benchmark three algrothims that construct regression models. To bechmark them I use cross-validation, so I obtain a matrix of errors (mean squared errors for example) with rows is number of cross-...
0
votes
0answers
23 views

How to use the off-diagonal terms of the covariance matrix when calculating confidence intervals?

The nonlinear fitting routine I use is MATLAB's fitnlm and it gives the covariance matrix. How can I take into account the off-diagonal values of this matrix to ...
1
vote
0answers
9 views

Setting bounds on multivariate data sets with possible multiple distribution types

Summary: I've got data sets whose distribution seems to differ based on where on the x-axis the data occurs. Using some common distribution mean and std dev calculations do not produce acceptable ...
0
votes
0answers
16 views

Assessing the residual independence assumption (nonlinear least squares regression diagnostics)

I would like to assess the assumptions underlying nonlinear regression models using statistical tests rather than graphical methods since I have thousands of fitting results. I am not certain ...
3
votes
0answers
28 views

Tips on how to improve a regression model

I'm developing a linear regression model (with nonlinear feature transforms) to fit some data. So far I've done the following things: I'm picking the parameter $\theta$ with the least (10-fold) cross-...