random

Simulate responses for nonlinear regression model

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Syntax

ysim = random(mdl)
ysim = random(mdl,Xnew)
ysim = random(mdl,Xnew,'Weights',W)

Description

ysim = random(mdl) simulates responses from the fitted nonlinear model mdl at the original design points.

ysim = random(mdl,Xnew) simulates responses from the fitted nonlinear model mdl to the data in Xnew, adding random noise.

example

ysim = random(mdl,Xnew,'Weights',W) simulates responses using the observation weights, W.

Examples

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Open Live Script

Create a nonlinear model of car mileage as a function of weight, and simulate the response.

Create an exponential model of car mileage as a function of weight from the carsmall data. Scale the weight by a factor of 1000 so all the variables are roughly equal in size. 

load carsmall
X = Weight;
y = MPG;
modelfun = 'y ~ b1 + b2*exp(-b3*x/1000)';
beta0 = [1 1 1];
mdl = fitnlm(X,y,modelfun,beta0);

Create simulated responses to the data. 

Xnew = X;
ysim = random(mdl,Xnew);

Plot the original responses and the simulated responses to see how they differ. 

plot(X,y,'o',X,ysim,'x')
legend('Data','Simulated')

Figure contains an axes object. The axes object contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Data, Simulated.

Input Arguments

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Nonlinear regression model, specified as a NonLinearModel object created using fitnlm.

Vector of real, positive value weights or a function handle.

  • If you specify a vector, then it must have the same number of elements as the number of observations (or rows) in Xnew.

  • If you specify a function handle, the function must accept a vector of predicted response values as input, and returns a vector of real positive weights as output.

Given weights, W, random estimates the error variance at observation i by MSE*(1/W(i)), where MSE is the mean squared error.

New predictor input values, specified as a table or matrix. Each row of Xnew corresponds to one observation, and each column corresponds to one variable.

  • If Xnew is a table, it must contain predictors that have the same names as predictors in the PredictorNames property of mdl.

  • If Xnew is a matrix, it must have the same number of variables (columns) in the same order as the predictor input used to create mdl. All variables used to create mdl must be numeric. To treat numerical predictors as categorical, specify the predictors using the CategoricalVars name-value argument when you create mdl.

Note that Xnew must also contain any predictor variables not used as predictors in the fitted model.

Data Types: single | double | table

Output Arguments

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Simulated response value, returned as a numeric vector. The simulated value is the predicted response values at Xnew perturbed by random noise. The noise is independent and normally distributed, with mean equal to zero and variance equal to the estimated error variance of the model.

Alternatives

For predictions without added noise, use predict.

Version History

Introduced in R2012a

See Also

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