Questions tagged [nonlinear]

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9
votes
4answers
4k 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 ...
6
votes
1answer
17k views

Fitting known equation to data

I have measured growth rates over a range of temperatures (temperature response curve) and would like to fit an already established equation/model to it. I'm very new to R and have trouble coding it ...
26
votes
1answer
10k views

Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression?

I have a question about semantics that I would like fellow statisticians' opinions on. We know models such as logistic, Poisson, etc. fall under the umbrella of generalized linear models. The model ...
14
votes
4answers
21k views

Distinction between linear and nonlinear model

I have read some explanations about the properties of linear vs nonlinear models, but still I am sometimes not sure if a model on hand is a linear or a nonlinear one. For example, is the following ...
23
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6answers
2k views

Advanced regression modeling examples

I'm looking for an advanced linear regression case study illustrating the steps required to model complex, multiple non-linear relationships using GLM or OLS. It is surprisingly difficult to find ...
8
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1answer
17k views

Non-linear SVM classification with RBF kernel

I'm implementing a non-linear SVM classifier with RBF kernel. I was told that the only difference from a normal SVM was that I had to simply replace the dot product with a kernel function: $$ K(x_i,...
6
votes
1answer
160 views

Pitfalls in Fitting Nonlinear Models by Transforming to Linearity

Some nonlinear models can be transform to linear models. My understanding is that there might be one-to-one relationship between the estimates of nonlinear model and its linear model form but their ...
6
votes
2answers
915 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 ...
5
votes
3answers
1k views

Nonlinear Statistics?

I have been studying Statistics recently, using a few introductory texts. My issue is these texts only seem to provide analysis methods that are suitable to linear relationships: Pearson r ...
5
votes
1answer
2k views

Is $R^2$ valid in a nonlinear model?

The question is in the title. The coefficient of determination or $ R^2 \equiv 1 - \frac{ss_{res}}{ss_{tot}} $ is valid in a nonlinear model? Why?
5
votes
2answers
8k views

Standard error of the quotient of two estimates (Wald estimators) using the delta method

I have two coefficients' estimates from a regression, each of which has an estimated standard error. I would like to know the quotient of these two estimates -- that is, divide one of the estimates by ...
1
vote
1answer
12k views

How can I account for a nonlinear variable in a logistic regression?

How can I account for a nonlinear independent variable in a logistic regression? For example, consider this data set: ...
2
votes
0answers
97 views

What is the nonlinear transformation assumed by the gaussian (rbf) kernel? [duplicate]

A common kernel choice is the gaussian kernel: $ k(x,x^{'}) = \exp \big( -\frac{1}{2\sigma^2}\| x - x^{'} \|^2 \big)$ This implies a transformation on $x$, and equally on $x^{'}$. What is it?
14
votes
1answer
5k views

Nystroem Method for Kernel Approximation

I have been reading about the Nyström method for low-rank kernel aproximation. This method is implemented in scikit-learn [1] as a method to project data samples to a low-rank approximation of the ...
17
votes
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 ...
18
votes
3answers
20k views

what makes neural networks a nonlinear classification model?

I'm trying to understand the mathematical meaning of non-linear classification models: I've just read an article talking about neural nets being a non-linear classification model. But I just realize ...
14
votes
3answers
18k views

Non-linearity before final Softmax layer in a convolutional neural network

I'm studying and trying to implement convolutional neural networks, but I suppose this question applies to multilayer perceptrons in general. The output neurons in my network represent the activation ...
13
votes
1answer
18k views

Why KNN is a non linear classifier ?

How do we decide if a classifier is linear or non linear ? What property/characteristic makes a classifier linear or non linear ? Eg: Why SVM is a linear classifier ? Why Logistic Regression is ...
10
votes
3answers
2k views

What are criteria and decision making for non-linearity in statistical models?

I hope that the following general question makes sense. Please keep in mind that for the purposes of this particular question I'm not interested in theoretical (subject domain) reasons for introducing ...
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 ...
13
votes
1answer
8k views

Explain steps of LLE (local linear embedding) algorithm?

I understand the basic principle behind the algorithm for LLE consists of three steps. Finding the neighborhood of each data point by some metric such as k-nn. Find weights for each neighbor which ...
8
votes
2answers
6k views

Goodness of fit for nonlinear model

We have fitted a nonlinear function to observed data. The next step should be the assessment of the goodness of fit of this function (like $R^2$ for linear models). What are the usual ways to ...
12
votes
3answers
2k views

Strategy for fitting highly non-linear function

For analyzing data from a biophysics experiment, I'm currently trying to do curve fitting with a highly non-linear model. The model function looks basically like: $y = ax + bx^{-1/2}$ Here, ...
5
votes
3answers
868 views

Can PCA be extended to account for nonlinear dependencies?

I have just learned principal component analysis, which seems to be an effective way to do dimension reduction. Now, I would like to know: Can PCA be extended to account for nonlinear dependencies? ...
2
votes
3answers
1k views

Pattern mining on a small data set

I have a small data set 30 features/predictors and 30 observations. My target variable is Oil production and my predictors are well & reservoir properties (depth, trajectory, temperature, pressure ...
6
votes
4answers
6k views

Nonlinear effect in an interaction term

If you have B, which is a 0/1 outcome variable, S, which is a continuous variable, and ...
4
votes
1answer
2k views

nonlinear meta-regression

Can someone point me to a basic explanation of theory and methods for fitting nonlinear curves (particularly quadratic functions) to meta-analytic data? I have a set of effect sizes that are clearly ...
2
votes
1answer
292 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
3answers
3k views

Confidence intervals for values estimated from the nonlinear regression model

I have a question about nonlinear regression and confidence intervals for values estimated from the model. Here is my problem. I have sets of data where $X$ is the logarithm of the dose of a chemical ...
6
votes
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 (...
4
votes
2answers
622 views

Can non-linear dependence be detected between two variables by regressing them?

Linear regression is meant for linear relationships right, so, if I don't trust linear correlation and want to find out if random variables $y$ and $x$ have a non-linear relationship, can't I just ...
3
votes
2answers
283 views

References on non-linear regression analysis [closed]

I am looking for the references on non-linear regression analysis. I am mostly interested in introductory textbooks focusing on theory, but covering some applications as well.
2
votes
0answers
879 views

Variance-covariance matrix

$\DeclareMathOperator{\var}{Var}$ How to compute prediction bands for non-linear regression? In the above link, you have mentioned about the variance-covariance matrix of the estimates. What is the ...
1
vote
2answers
6k views

How to test for multicollinearity among non-linearly related independent variables

I have a health outcome (measured as a rate of cases per 10,000 people in an administrative zone) that I'd like to associate with 15 independent variables (social, economic, and environmental measures ...
1
vote
2answers
353 views

How to analyze curvilinear seasonal data

I have monthly values of a continuous variable from many subjects, the mean of which on plotting show curvilinear pattern with lower values in summer months. How can I analyze and report the ...
1
vote
2answers
167 views

Resource request : How to prove the output of a process is random variables?

I am reading through articles which present the spectral properties of chaotic systems such that they can be candidates for generating pseudo random binary sequences. One such article, is http://...
0
votes
0answers
119 views

How to use a scatter plot to detect non-linear co-dependence between two variables?

A scatter plot matrix of 3 time series (financial returns data) are shown below. It is a multivariate representation of a scatter plot, with the individual pairs shown in the off-diagonals. The ...
0
votes
1answer
874 views

R lmer, 3 time point longitudinal data, non linear, messy residual help!

I am new to mixed models so please go easy on me! I am attempting to longitudinally model a normally distributed continuous outcome with values in my dataset from -30-10. I have data collected at 1, ...