# Questions tagged [nonlinear]

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### Regression with flexible functional form

I am assuming a model of the form $$Y_i=\alpha+\beta X_i+g(\mathbf{Z}_i)+\epsilon_i,$$ here $\mathbf{Z}_i$ is an $m$ dimensional vector and $\epsilon_i$ is i.i.d. white noise. I would like to ...
77 views

### Correlation is a symmetric measure, but scatter plot matrix shows asymmetric dependence

The correlation matrix demonstrates that correlation is a symmetric measure: $\rho(X,Y) = \rho(Y,X)$ since the lower off-diagonals are mirror images of the upper off-diagonals. The scatterplot matrix ...
30 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 ...
528 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 ...
2k views

### What is the best programmatic way for determining whether two variables are linearly or non-linearly or not even related

What is the best programmatic way for determining whether two predictor variables are linearly or non-linearly or not even related, maybe using any of the packages scipy/statsmodels or anything else ...
23 views

### Logistic Regression on Non-linear Boundary [duplicate]

How should we expect logistic regression to perform on a dataset of 2 classes separated by a non-linear decision boundary like the unit circle? My understanding is that accuracy will most likely be ...
20 views

### Does a low correlation level warrant the need to try a different dependence measure?

Can it be determined somehow whether the correlation coefficient between two random variables would be insufficient for assessing the level and type of co-dependency between them, and that another ...
22 views

### Solving a system of nonlinear equations involving only products of unknowns

I would like to find the solution of a system of equations of the form: $A = w_1 F(x_k) + w_2 F(x_l) + w_3 F(x_m) +...$, where the unknowns are the $w_i$ and the function $F$, while my data are the $A$...
23 views

### Stopped by zero step from line search - R stops optimization early

I am trying to minimize an objective function, $J(\theta)$, with respect to $\theta$, a 19-dimensional parameter vector. $J(\theta)$ is a smooth nonlinear function so I have tried various gradient-...
68 views

### How come covariance can pick up non-linear relationships but correlation can't? [closed]

correlation is computed from covariance so how come covariance can pick up non-linear relationships between variables $X$ and $Y$ but (Pearson's) correlation can't?
67 views

### Neural Network: Matlab uses different activation functions for different layers - why?

I have trained on matlab an Artificial Neural Network with one input layer, one hidden layer and one output layer (my output is values between zero and one, which I turn into 0 or 1 according to a ...
6 views

### Expectation of truncated autoregressive process

Consider the following nonlinear autoregressive model: \begin{align*} \epsilon_t & = \epsilon^\rho_{t-1} e^{u_t}, \\ x_t & = \frac{\gamma \, \epsilon_t x^a_{t-1}}{1+b y_t}, \\ y_t & = \...
14 views

### How to detect non-linearity between two time series?

What approaches are there for detecting the existence of a non-linear co-dependency or relationship between two non-monotonic random variables or time series? Given two time series, I want to know ...
14 views

### How to decompose entropy into linear and non-linear components?

Mutual information is the entropy between two random variables, $X$ and $Y$, based on their probabilities. It captures both the linear and non-linear interactions between $X$ and $Y$, whereas ...
52 views

### Non-Linear Time Series Book

I am looking for a book to study non linear time series for both univariate and multivariate topics. Your suggestions will be greatly appreciated. Thanks.
25 views

### Augmented Dickey Fuller and Nonlinear Time Series

Since the Augmented Dickey Fuller test assumes the time series to be an autoregressive-moving average model, I was wondering if it would be possible to explicitly construct a nonlinear time series ...
28 views

### How to determine the influence of a variable on the relationship between another two variables?

I have three continuous variables X, Y, and Z in the form of timeseries at several geographic locations. All variables have a skewed distribution because the timeseries mostly have zeros in them ...
16 views

### How to perform time series prediction for small time series in rstudio using gam model?

I have a dataset which contains year(4 years - 2016, 2017, 2018, 2019), yield, ndvi, ndre,... savi indices, latitude and longitude of a field area of 8 hectacre. I have to predict the yield potential ...
53 views

### What are options if Rainbow test fails after Linear Regression

I tested with commonly available iris dataset and ran OLS with following formula: PW ~ SW + PL + SL + Species Output is as follows: ...
222 views

### Why not always use generalized estimating equations (GEE) instead of linear mixed models?

I read about generalized estimating equations (GEE) here, here and at other sites. It is mentioned in first of above links that "the parameter estimates are nearly identical" for linear ...
10 views

### Difference between sequential/simultaneous nonlinear partial least squares and NIPALS algorithm

I've been reading about nonlinear partial least squares, and according to the below study, there are two types of NLPLS: sequential NLPLS and simultaenous NLPLS. https://www.sciencedirect.com/science/...
48 views

### Nonlinear minimum Mean Square Error estimation

Let say I have the following parameter to estimate: $$\theta = \frac{1}{\mu^2 - 1} \ .$$ The observed measurement is $x \sim \mathcal{N}(\mu,\sigma)$. The mean $\mu$ is unknown. There are two cases I ...
33 views

### When does a Linear regression stop being a good fit?

I'm testing a couple of hypotheses and I have a non normally distributed continuous response variable (residuals are not normally distributed as well). I have been given mixed suggestion on what model ...
412 views

### Effect of nonlinear transformations on the mean

Suppose I have a continuous random variable $X$ and a random variable $Z = f(X)$, where $f$ is a nonlinear monotonic transformation. How can I prove the following relation between the mean and the ...
26 views

### Linear Or Non-Linear Relationship?

I am confused as to whether relationship between height (y) and weight (x) in the graph below is linear? As my assumption is if we fit a regression line, it wont be a good fit as one x value has ...
16 views

### Ideal copula family to evaluate a joint CDF of a process with non-linear dependency?

Say a process exhibits ARCH/GARCH type non-linear dependence and we wish to evaluate its joint CDF. Without relying on a criterion, such as AIC what is the best copula family that fits this framework? ...
31 views

### Statistical Testing of Non-linear Model Parameters

I have produced three non-linear 4-parameter logistic curves based on some experimental observations using three different measurement devices. Each curve shows the measurement of density decline ...
15 views

### Modeling data coming from different sensors

Let us say that we measure a continuous phenomenon Y with multiple sensors. Despite the calibration process, we expect that the responses of the sensors are not exactly the sames. Some will have a ...
13 views

### Transformation to linear regression. Help!

There is one problem where a regression is like this 𝑦𝑖 = (𝛼 + 𝛽𝑥𝑖)*𝜀. How could I get the OLS estimator? Maybe trying a transformation? I just trying by taking log, but still no result. Also, ...
75 views

### How do I evaluate correlation, that appears non-linear

Directed here from StackOverflow Let's say I want to assess if there is a correlation between two fields, one of which I know to have a power distribution. A lot of the information I read assumes ...
24 views

### L-BFGS-B. Forces early stop with no 0 gradient

I am minimizing a non-linear function which is close to linear with L-BFGS-B with scipy.optimize. The issue is that I have a non zero jacobian, low levels of tolerance but the algorithm keeps early ...
26 views

### Granger causality test - What dependencies are being captured?

I'm currently reading on the Granger causality test but different sources seem to be contradicting. In the original paper Using the mutual information coefficient to identify lags in nonlinear models ...
11 views

### Libraries for non-linear PCA visualization

Are there any open-source python libraries or repositories that can be used to create nonlinear biplots? Or, more generally, are there open-source python libraries to visualize non-linear PCA or VAE ...
30 views

### Q, method for non-linear mixed effect model using nlme?

I'm trying to apply non-linear mixed effect model in my data, but it does not work at all. My code is, ...
96 views

### How to calculate confidence intervals of non linear sigmoidal fitting curve?

I'm not using R or any other stats framework, I'm trying to implement myself an algorithm to optimize the fitting curve and to calculate the EC50 confidence intervals. Problem I have is my lack of ...
20 views

### Nonlinearity of Neural Networks [duplicate]

Most books and articles often refer to Neural Networks as capturing nonlinear relationships between the dependent and independent variables, as well as allowing for interactions between the ...
38 views

### Optimization equivalence

Can someone help me with the step by step demonstration of the following equivalence used in SVM: $$maximize: m = \frac{1} {\|w\|} \equiv minimize: m =\frac{1} {2}\|w\|^2$$ I would be most grateful ...
44 views

### Including a quadratic effect for an ordinal variable in a regression analysis

It's common for many datasets to have ordinal versions of numerical variables, such as age groups (e.g. "Under 20", "20-30", "30-40", etc.) or time groups (e.g. "Less than 15 minutes", "15-30 minutes",...
13 views

### Will using an interaction dummy give the same estimate as stratifying by that category for non-linear regressions?

I know that with linear; $Y = A_1 + A_2D + B_1X + B_2X*D$ that $A_1 + A_2 = C_1$ and $B_1 + B_2 = E_1$ where $Y = C_1 + E_1X$ | stratified over $D = 1$ But I can't seem to replicate my results ...
27 views

### Binary Non Linear Regression with Time Series and Group Interaction Effect

First post so I'll try to be as specific as possible. My design is as follows: 2 groups: Control and Treatment 5 min test of movement within an arena with a zone of interest Binary Dependent ...
26 views

### If the Lagrangian formulation also has constraints, what is then the simplification?

Consider the following constrained optimization problem. $$\begin{array}{ll} \text{minimize} & f(w)\\ \text{subject to} & g_{i}(w) \leq 0\\ & h_{j}(w) = 0\end{array}$$ The equivalent ...
53 views

### Can linear (Pearson) correlation overestimate the true value?

It's well known that Pearson correlation can underestimate the true value in case of non-linear relationship. But can it overestimate? For example, Pearson correlation of discontinuous distributions, ...
32 views

### Machine learning methods for panel data

I have a panel data in which I have time series value for a particular stock with multiple features. Similarly, I have such datasets for multiple stocks, the features are consistent across stocks(...
33 views

### Jacobian for function including cubic spline

I am trying to fit a measured spectrum with a linear combination of end-member spectra which are approximated by cubic spline functions ($f_1$ and $f_2$). I also need to incorporate terms that account ...
173 views

### Can I use *any* activation function in my Neural network as long as it is non-linear?

I am currently learning about Neural networks and am finding it hard to comprehend the reason why activation functions such as ReLU or sigmoid are favored. In general, I understand the need for the ...
13 views

### Specifying interactions in nonlinear growth curve models

I have a nonlinear growth curve model with Time and Time^2 as well as one time-varying predictor (level 2) and one time-invariant variable (level1). I want to test interaction effects. Normally I ...
14 views

### Nonlinear relationship in logistic regression [duplicate]

I have a binary dependent variable (infection + or -) and both continuous and categorical independent variables. One continuous independent variable (BMI) seems to be nonlinear in that the lowest and ...
10 views

### Options for nonparametric preference ranking models

What are some options for nonparametric ranking models with a probabilistic interpretation? I'm basically looking for a nonlinear/nonparametric version of a rank ordered logit model. I'm aware of ...