Questions tagged [nonlinear]

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4answers
3k views

Is R-squared truly an invalid metric for non-linear models?

I have read that R-squared is invalid for non-linear models, because the relationship that SSR + SSE = SSTotal no longer holds. Can somebody explain why this is true? SSR and SSE are just the ...
1
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1answer
445 views

Is log-log model considered to be nonlinear?

I am currently revising a paper, in which I tested an empirical model in the following form: , where EP is indicator of environmental performance, FDI - foreign direct investment which is the main ...
1
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0answers
48 views

Do I need to check for heteroskedasticity/heteroscedasticity only when performing regression analyses?

I don't know if this is a silly question but I haven't been able to find precise answer anywhere. I'm building a linear regression model in R to predict a variable of interest $y$, but there are also ...
6
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2answers
906 views

UMVU estimator for non-linear transformation of a parameter

Let $X_1, ..., X_n$ be iid. and $X_1\sim N(\mu,1)$. $\gamma(\mu)=e^{t\mu}$ for $t\neq 0$ My question is how to find an UMVU estimator for $\gamma(\mu)$ My concern is not so much about the specific ...
3
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1answer
2k views

Standard errors for non-linear least squares in R

I have a question on standard errors for non-linear least squares in R. With the built-in function NLS and a hand-made function I get different SE and I don't understand why. I will try to expose ...
1
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2answers
451 views

Nonlinear regressor in GLM link function

Try to reproduce Robert E. McCulloch and Ruey S. Tsay’s paper Nonlinearity in High-Frequency Financial Data and Hierarchical Models with local market data. the paper uses GLM to model high-frequency ...
6
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3answers
193 views

General approaches and techniques for developing good explanatory models for nonlinear data

Various recent efforts of mine on modelling some data through logistic regression have been... not successful. While there is still more data to look at, I've been wanting to explore nonlinear ...
1
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1answer
76 views

What data format should I use to learn the nonlinear output behavior of my guitar distortion pedal using a neural networkl?

My Problem I've built a very simple transistor guitar pedal. it has 1 mono input, 1 mono output. Now, all I have ever done in the past with ANN's is offline learning with labelled data and some work ...
4
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1answer
431 views

Non-linear relationship among independent variables in linear model

Assume that we have a linear model with 4 independent variables, and 2 of them have a strong non-linear relationship (between them). How this fact could affect my model ($R^2$, or implications on the ...
0
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0answers
141 views

Singular value decomposition

Can singular value decomposition used to impute missing values in highly nonlinear process under multiple input and multiple output behavior?
17
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1answer
2k views

If an auto-regressive time series model is non-linear, does it still require stationarity?

Thinking about using recurrent neural networks for time series forecasting. They basically implement a sort of generalized non-linear auto-regression, compared to ARMA and ARIMA models which use ...
1
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1answer
219 views

Using Iterative Gradient Descent to Determine to determine the Transformation for a Registration Algorithm

Based on the paper "Iterative Estimation of Rotation and Translation using the Quaternion" I am trying to define find the transformation, i.e. the rotation and scaling, that registers points from the ...
-1
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1answer
404 views

Non-linear VS non-normal

Are they same? I know they are absolutely different due to the different concept, but a paper said they are same. Is it true?
0
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1answer
89 views

Is my model linear or non-linear

I was going through the following discussions Is this a linear or non linear model, and why? How to identify models as linear or non-linear? In the above discussions, users have submitted some ...
1
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1answer
332 views

Identification of a Heckman Model through Nonlinearity

I often read that the standard Heckman selection model is identified from the non-linearity of the Mill’s ratio. I don’t fully understand why linearity (or lack of) determines identification. From ...
6
votes
1answer
5k views

What exactly happens when I do a feature cross?

I was going through a machine learning course and they talked about combining various features to create synthetic feature to take care of non linear data. For eg in the below picture I didn't do any ...
1
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0answers
61 views

Non linear high-dim equations solving - Quasi-MLE

Equations : I'm trying to find the best way of estimating the parameters of the following equations : Knowing the value of $n$ (in my case $n=27$), Knowing the values of constants $(a_i)_{i \in \{1,...
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0answers
39 views

How to test to the null that the two asymptotes are the same?

Consider the following dummy data (in R) ...
1
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0answers
128 views

Endogeneity of variables in non-linear prediction models

I am new to R and try to predict customer returns for unknown data based on a known dataset. For feature selection and engineering I used the Random Forest (RF) based importance scores, which showed ...
1
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0answers
60 views

Choosing a robust kernel based on dataset properties (theoretical arguments)

Consider a non-linear least squares estimation problem, where we use a kernel (i.e. M-estimator) to reduce sensitivity to outliers,e.g. $argmin_x \sum\limits_{k=1}^n\rho_k(||r_k(x)||_2)$, where $...
1
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0answers
101 views

The difference between systems with and without direct feedthrough

Generally, in nonlinear state estimation the state space model is defined by the following pair of difference equations in discrete-time: \begin{equation} \begin{aligned} x_k & = f(x_{k-1},u_{k-1}...
1
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1answer
40 views

Correlation of a product

Suppose we have three random variables X, Y, T. X is positively correlated with T: we know $\rho_{XT}$ and it is greater than 0, let's say for the sake of argument 0.5. Y is positively correlated ...
0
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0answers
236 views

Nonlinear transformation vs Nonlinear regression

Apologies, if the question has some error since my knowledge of statistics is limited. I am trying to predict DV using 9 IV. Using curve fit option in SPSS, I am finding that 6 of my IV have higher $R^...
3
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1answer
1k views

Choosing a nonlinear model: GAM?

I have the response variable that is an abundance matrix Y. for example, I have four columns with species 1 species 2 species 3 and species 4 abundances at each location (each location is separate ...
0
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1answer
219 views

coefficient of Nonlinear relationship interpretation

I try to identify a nolinear relationship between a dependent variable and independent varaibles. In the literature, to detect this relation, we introduce the term. When I make a simple Regression ( ...
0
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1answer
54 views

Calculating t-value for regression coefficients

I am estimating a nonlinear model as follows: $$Y=B_0+B_1X_1+B_2X_2+B_3aX_3^{1-b}+B_4$$ I have estimated $B_0$, $B_1$, $B_2$, $B_3$, $B_4$, $a$, and $b$ using least squares in Excel (minimizing SSR ...
6
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1answer
272 views

If in this problem I regress $x$ on $y$ instead than $y$ on $x$, do I need to use an error-in-variables model?

I was trying to write an answer for this question: Selection of data range changes coefficients too much in lmer (inverse regression) Basically the OP has lots of data of Amplification vs Voltage (...
1
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0answers
2k views

How to model a dependent variable with a U-shaped dependent variable?

Note: I should have flipped x and y in this example to be in line with typical notation. Sorry for any confusion. Consider the ...
4
votes
2answers
682 views

How to fit a poisson glm in R when the parameters are not separated

I am trying to fit a poisson GLM to count data. Where the count $N_r$ for time $t_r$ is assumed to follow $\mathrm{ Poisson} (\lambda (t_r - t_0)^{-\alpha} e^{-\beta t_r})$. Here $r$ is discrete ...
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1answer
2k views

What are the Advantages of R over Python in Statistics? [duplicate]

So I'm a budding quant, but came from an Economics background so what I learned first was R and, of course, have fallen in love ever since. However, I recently started doing research on why Python ...
2
votes
1answer
370 views

Multivariate Solutions to Nonlinear Data

I've been surveying the different methods of approaching linear multivariate problems (ex PCA, PLS, factor analysis etc.) and want generate a model for Y's that depend non-linearly on $X$'s via ...
1
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1answer
235 views

Logistic Regression Odd Ratio Linearity

I'm at the exploratory stage of a logistic regression model. The outcome is saying yes or no to a particular offer and the independent variable I'm currently investigating is the age of the customer. ...
0
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1answer
130 views

Check for Non-Linear Relationship between Continuous Independent and Ordinal Dependent Variables

Lets say I have age as the independent variable; education (1=college; 2=masters; 3=phd) and employment (1=unemployed; 2=part-time; 3=full-time) are the dependent variables. If I was trying to check ...
1
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0answers
238 views

What are the statistical properties of average partial effect in nonlinear models?

Using a linear model like OLS, the marginal effects are simply the coefficients given by $\beta = (X'X)^{-1}X'y$. However, in a nonlinear model, it is more difficult to derive marginal effects. For ...
2
votes
3answers
117 views

Which function fits this data?

I have collected this empirical data, and would like to know which function describes this data (3 curves) at best. I have try non linear fit in R, but not good fit. How can I discover the relation ...
2
votes
1answer
475 views

The effect of nonlinearity trends in the data on the cross correlation

Assume we have two datasets $X$ and $Y$ and I want to evaluate the cross correlation between them. What are the effects of nonlinearity trends within each dataset? That is, are there any relations ...
3
votes
1answer
577 views

dimensioality reduction: Sammon Mapping

Reversing linear dimensionality reduction algorithms by projecting new set of data in the learned manifold is very straight forward. I am interested in projecting new set of data on non-linear ...
0
votes
1answer
81 views

Why is necessary non-linear model?

I think linear model is such as linear regression, logistic regression (including one with polynomial features), SVM (including one with kernel). I think non-linear model is such as decision tree, ...
1
vote
0answers
51 views

Nonlinear Structural Equation Modelling- Estimation via Pseudo Maximum Likelihood in R

I am trying to implement the pseudo maximum likelihood approach described in Wall and Amemiya (2007) (see link to article at the end) in estimating the parameters of a nonlinear structural model of ...
2
votes
1answer
291 views

Is this a linear or non linear model, and why?

A model $Y=(\beta_0+\beta_1x)^{-1}+\epsilon$, where $\epsilon \sim N(0,\sigma^2)$ is to be fitted to the data $(x_1,Y_1), (x_2,Y_2), \dots (x_n,Y_n)$. Is this a linear or non linear model, and why? ...
0
votes
1answer
421 views

Interpreting a regression equation with summation notaion

I am definitely more of an applied statistician than one with a strong background in the specific mathematical notation. I'd like to recreate a model I ran across in a paper, and though I understand ...
1
vote
0answers
282 views

Looking for candidate functions for a “flat top” bell-shaped curve [duplicate]

I am looking for some candidate functions to model some data that is somewhat bell shaped, but more flat at the top - something like this: I was previously using two sigmoid functions, flipping one, ...
4
votes
1answer
88 views

Classification where we are more confident in some training samples than others [duplicate]

Let's say we have a supervised learning binary classification dataset. We are a lot more confident in some training examples than in others being accurate (e.g. some were labelled by several highly ...
10
votes
2answers
2k views

Is autocorrelation in a supervised learning dataset a problem?

Imagine the following problem. I have weekly snapshots of price data of K items, as well as of various features/predictors. I want to predict how much the price will change 2 years from now. I ...
0
votes
0answers
290 views

Does PCA ahead of an Autoencoder deter it from detecting non-linearity?

PCA is recommended before AE for uncorrelating the inputs (ref). Autoencoders being neural networks, they're good for non-linear dimensionality reduction (wikipedia). PCA is a linear technique With ...
0
votes
1answer
102 views

Obtain outcome after log-transform [duplicate]

I have to get a regression model for a dataset, and it seems that the best fit is obtained by log transforming the outcome, so that I simply applied the least squares on the trasformed response vector....
1
vote
0answers
300 views

Measuring MSE on log-linear model

I have to get a regression model for a dataset, and it seems that the best fit is a log-linear model, so that I simply applied the least squares on the trasformed response vector. $ log(\hat{Y}) = f(...
1
vote
0answers
289 views

Error propagation through a nonlinear model with error on constants as well as observations

I'm using the following equation to invert (non-linearly) for three parameters, L Vr and f. $$T_r=\frac{L}{V_r} - \frac{(L\,\cos( \theta )\,\cos( \alpha - f))}{V} $$ I have observational errors on $...
2
votes
0answers
45 views

How to predict trajectory of a stochastic process under a nonlinear mapping?

I have a nonlinear model $$N_{t+1} = r N_t \exp (-N_t)$$ with some simulated values $$N^*_{t+1} = r N_t \exp (-N_t+ \varepsilon_{t+1}) $$ $N^*_t$ (having independent errors $\varepsilon_t$ ...
1
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0answers
471 views

Penalized spline/mixed model

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