MATLAB: Prediction Slice plot – what are the numbers inside the brackets on the left

diagnostic plotsglm

I ran a glm model with 4 dependent variables and one predicted variable (binary response). Then I plotted the Slice plots. I think I can understand that the prediction on the left is the value expected at the set values shown below each of the predictors. How ever I don't understand what the numbers inside the brackets on the left represent. Also, what is the difference between "simultaneous and no-simultaneous" bonds? (I noticed the numbers on the brackets change accordingly)

Thanks, Karina

Best Answer

The bracketed numbers are 95% confidence limits on the predicted value of the dependent variable at the chosen point.

I can’t find the ‘simultaneous and non-simultaneous bounds’ specifically mentioned in the documentation (the closest I can get is Plots to Understand Predictor Effects). They seem to consider the effect of all the independent (predictor) variables as opposed to each individual independent (predictor) variable on the dependent (response) variable. This is consistent with the confidence intervals being narrowest with the ‘non-simultaneous’ option.

I’m reasonably confident about the bracketed numbers, because looking at the plot, the numbers correspond to the plotted confidence interval. We’ll likely have to wait for MathWorks to see this and confirm it to be certain about my ‘bounds’ interpretation.

Related Solutions

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')))

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

Best Answer

Related Solutions

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

MATLAB: Estimate confidence intervals after regress!

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