MATLAB: Multi level regression analysis

mixed effect regression analysismulti level regression analysis

Hi All,

Are there functions available (maybe in a toolbox) that allow me to perform a multi level (aka mixed effect) regression analysis?

(A multiple regression analysis is availabe, that I know)

Thanks,

R.,

Koen

Best Answer

Statistics Toolbox includes two different algorithms (nlmefit and nlmefitsa) for fitting nonlinear mixed effects model.

nlmefitsa uses stochastic expectation maximization.

beta = nlmefit(X,y,group,V,fun,beta0) fits a nonlinear mixed-effects regression model and returns estimates of the fixed effects in beta. By default, nlmefit fits a model in which each parameter is the sum of a fixed and a random effect, and the random effects are uncorrelated (their covariance matrix is diagonal).

[BETA,PSI,STATS,B] = nlmefitsa(X,Y,GROUP,V,MODELFUN,BETA0) fits a nonlinear mixed-effects regression model and returns estimates of the fixed effects in BETA. By default, nlmefitsa fits a model where each model parameter is the sum of a corresponding fixed and random effect, and the covariance matrix of the random effects is diagonal, i.e., uncorrelated random effects.

The BETA, PSI, and other values this function returns are the result of a random (Monte Carlo) simulation designed to converge to the maximum likelihood estimates of the parameters. Because the results are random, it is advisable to examine the plot of simulation to results to be sure that the simulation has converged. It may also be helpful to run the function multiple times, using multiple starting values, or use the 'Replicates' parameter to perform multiple simulations.

Related Solutions

MATLAB: Estimate confidence intervals after regress!

The ‘BINT’ matrix contains the parameter confidence intervals.

If you want both parameter and prediction confidence intervals, use fitlm:

x = (1:10)';                                        % Create Data

y = 1.5 + 2.3*x + 1.5*randn(size(x));               % Create Data
mdl = fitlm(x, y);                                  % Fit Data
B = mdl.Coefficients.Estimate;                      % Coefficients
CI = coefCI(mdl);                                   % Coefficient Confidence Intervals
[Ypred,YCI] = predict(mdl, x);                      % Fitted Regression Line & Confidence Intervals
figure(1)
plot(x, y, 'pg')
hold on
plot(x, Ypred,'-r',    x, YCI, '--r')
hold off
grid

MATLAB: How does plotslice used to analyze generalized linear models generate simultaneous confidence bounds

I'm not sure how you are comparing intervals from coefCI, which are for the coefficients, and intervals from plotSlice, which are for predictions.

The plotSlice function just computes predictions and confidence bounds for them. Here are some examples of how to reproduce those same things by hand. Remember to invert the logistic function when you compute predictions.

% example from "help fitglm"
load hospital
formula = 'Smoker ~ Age*Weight*Sex - Age:Weight:Sex';
glm = fitglm(hospital,formula,'distr','binomial');
% Get predictions and confidence intervals
[pred,ci] = predict(glm,hospital(1,:))
% calculate those by hand
b = glm.Coefficients.Estimate;
C = glm.CoefficientCovariance;
x = [1 1 38 176 38 176 38*176]; % from first row of hospital data
mypred = 1./(1+exp(-x*b))
myci = 1./(1+exp(-x*b + [1 -1] * 1.96*sqrt(x*C*x')))
% compute the plotslice default (simultaneous) intervals by hand
simci = 1./(1+exp(-x*b + [1 -1] * sqrt(chi2inv(.95,7))*sqrt(x*C*x')))

Best Answer

Related Solutions

MATLAB: Estimate confidence intervals after regress!

MATLAB: How does plotslice used to analyze generalized linear models generate simultaneous confidence bounds

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