glmval

Generalized linear model values

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Syntax

yhat = glmval(b,X,link)
[yhat,dylo,dyhi] = glmval(b,X,link,stats)
[...] = glmval(...,param1,val1,param2,val2,...)

Description

yhat = glmval(b,X,link) computes predicted values for the generalized linear model with link function link and predictors X. Distinct predictor variables should appear in different columns of X. b is a vector of coefficient estimates as returned by the glmfit function. link can be any of the character vectors, string scalars, or custom-defined link functions used as values for the 'link' name-value pair argument in the glmfit function.

Note

By default, glmval adds a first column of 1s to X, corresponding to a constant term in the model. Do not enter a column of 1s directly into X. You can change the default behavior of glmval using the 'constant' parameter.

[yhat,dylo,dyhi] = glmval(b,X,link,stats) also computes 95% confidence bounds for the predicted values. When the stats structure output of the glmfit function is specified, dylo and dyhi are also returned. dylo and dyhi define a lower confidence bound of yhat-dylo, and an upper confidence bound of yhat+dyhi. Confidence bounds are nonsimultaneous, and apply to the fitted curve, not to a new observation.

[...] = glmval(...,param1,val1,param2,val2,...) specifies optional parameter name/value pairs to control the predicted values. Acceptable parameters are listed in this table:

ParameterValue

'confidence' — the confidence level for the confidence bounds

A scalar between 0 and 1

'size' — the size parameter (N) for a binomial model

A scalar, or a vector with one value for each row of X

'offset' — used as an additional predictor variable, but with a coefficient value fixed at 1.0

A vector

'constant'

  • 'on' — Includes a constant term in the model. The coefficient of the constant term is the first element of b.

  • 'off' — Omit the constant term

'simultaneous' — Compute simultaneous confidence intervals (true), or compute non-simultaneous confidence intervals (default false)true or false

Examples

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Open Live Script

Fit a generalized linear regression model, and compute predicted (estimated) values for the predictor data using the fitted model.

Create a sample data set. 

x = [2100 2300 2500 2700 2900 3100 ...
     3300 3500 3700 3900 4100 4300]';
n = [48 42 31 34 31 21 23 23 21 16 17 21]';
y = [1 2 0 3 8 8 14 17 19 15 17 21]';

x contains the predictor variable values. Each y value is the number of successes in the corresponding number of trials in n.

Fit a probit regression model for y on x. 

b = glmfit(x,[y n],'binomial','Link','probit');

Compute the estimated number of successes.

yfit = glmval(b,x,'probit','Size',n);

Plot the observed success percent and estimated success percent versus the x values.

plot(x,y./n,'o',x,yfit./n,'-')

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

Open Live Script

Enter sample data. 

x = [2100 2300 2500 2700 2900 3100 ...
     3300 3500 3700 3900 4100 4300]';
n = [48 42 31 34 31 21 23 23 21 16 17 21]';
y = [1 2 0 3 8 8 14 17 19 15 17 21]';

Each y value is the number of successes in corresponding number of trials in n, and x contains the predictor variable values.

Define three function handles, created by using @, that define the link, the derivative of the link, and the inverse link for a probit link function,. Store the handles in a cell array.

link = @(mu) norminv(mu);
derlink = @(mu) 1 ./ normpdf(norminv(mu));
invlink = @(resp) normcdf(resp);
F = {link, derlink, invlink};

Fit a generalized linear model for y on x by using the link function that you defined. 

b = glmfit(x,[y n],'binomial','link',F);

Compute the estimated number of successes. Plot the observed and estimated percent success versus the x values.

yfit = glmval(b,x,F,'size',n);
plot(x, y./n,'o',x,yfit./n,'-','LineWidth',2)

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

This example uses:

Open Script

Train a generalized linear model, and then generate code from a function that classifies new observations based on the model. This example is based on the Use Custom-Defined Link Function example.

Enter the sample data.

x = [2100 2300 2500 2700 2900 3100 ...
     3300 3500 3700 3900 4100 4300]';
n = [48 42 31 34 31 21 23 23 21 16 17 21]';
y = [1 2 0 3 8 8 14 17 19 15 17 21]';

Suppose that the inverse normal pdf is an appropriate link function for the problem.

Define a function named myInvNorm.m that accepts values of $X\beta$ and returns corresponding values of the inverse of the standard normal cdf.

function in = myInvNorm(mu) %#codegen
%myInvNorm Inverse of standard normal cdf for code generation
%   myInvNorm is a GLM link function that accepts a numeric vector mu, and
%   returns in, which is a numeric vector of corresponding values of the
%   inverse of the standard normal cdf.
%   
in = norminv(mu);
end

Define another function named myDInvNorm.m that accepts values of $X\beta$ and returns corresponding values of the derivative of the link function.

function din = myDInvNorm(mu) %#codegen
%myDInvNorm Derivative of inverse of standard normal cdf for code
%generation
%   myDInvNorm corresponds to the derivative of the GLM link function
%   myInvNorm. myDInvNorm accepts a numeric vector mu, and returns din,
%   which is a numeric vector of corresponding derivatives of the inverse
%   of the standard normal cdf.
%   
din = 1./normpdf(norminv(mu));
end

Define another function named myInvInvNorm.m that accepts values of $X\beta$ and returns corresponding values of the inverse of the link function.

function iin = myInvInvNorm(mu) %#codegen
%myInvInvNorm Standard normal cdf for code generation
%   myInvInvNorm is the inverse of the GLM link function myInvNorm.
%   myInvInvNorm accepts a numeric vector mu, and returns iin, which is a
%   numeric vector of corresponding values of the standard normal cdf.
% 
iin = normcdf(mu);
end

Create a structure array that specifies each of the link functions. Specifically, the structure array contains fields named 'Link', 'Derivative', and 'Inverse'. The corresponding values are the names of the functions.

link = struct('Link','myInvNorm','Derivative','myDInvNorm',...
    'Inverse','myInvInvNorm')

link = 

  struct with fields:

          Link: 'myInvNorm'
    Derivative: 'myDInvNorm'
       Inverse: 'myInvInvNorm'

Fit a GLM for y on x using the link function link. Return the structure array of statistics.

[b,~,stats] = glmfit(x,[y n],'binomial','link',link);

b is a 2-by-1 vector of regression coefficients.

In your current working folder, define a function called classifyGLM.m that:

  • Accepts measurements with columns corresponding to those in x, regression coefficients whose dimensions correspond to b, a link function, the structure of GLM statistics, and any valid glmval name-value pair argument

  • Returns predictions and confidence interval margins of error

function [yhat,lo,hi] = classifyGLM(b,x,link,varargin) %#codegen
%CLASSIFYGLM Classify measurements using GLM model 
%   CLASSIFYGLM classifies the n observations in the n-by-1 vector x using
%   the GLM model with regression coefficients b and link function link,
%   and then returns the n-by-1 vector of predicted values in yhat.
%   CLASSIFYGLM also returns margins of error for the predictions using
%   additional information in the GLM statistics structure stats.
narginchk(3,Inf);
if(isstruct(varargin{1}))
    stats = varargin{1};
    [yhat,lo,hi] = glmval(b,x,link,stats,varargin{2:end});
else
    yhat = glmval(b,x,link,varargin{:});
end
end

Generate a MEX function from classifyGLM.m. Because C uses static typing, codegen must determine the properties of all variables in MATLAB® files at compile time. To ensure that the MEX function can use the same inputs, use the -args argument to specify the following in the order given:

  • Regression coefficients b as a compile-time constant

  • In-sample observations x

  • Link function as a compile-time constant

  • Resulting GLM statistics as a compile-time constant

  • Name 'Confidence' as a compile-time constant

  • Confidence level 0.9

To designate arguments as compile-time constants, use coder.Constant.

codegen -config:mex classifyGLM -args {coder.Constant(b),x,coder.Constant(link),coder.Constant(stats),coder.Constant('Confidence'),0.9}

Code generation successful.

codegen generates the MEX file classifyGLM_mex.mexw64 in your current folder. The file extension depends on your system platform.

Compare predictions by using glmval and classifyGLM_mex. Specify name-value pair arguments in the same order as in the -args argument in the call to codegen.

[yhat1,melo1,mehi1] = glmval(b,x,link,stats,'Confidence',0.9);
[yhat2,melo2,mehi2] = classifyGLM_mex(b,x,link,stats,'Confidence',0.9);

comp1 = (yhat1 - yhat2)'*(yhat1 - yhat2);
agree1 = comp1 < eps
comp2 = (melo1 - melo2)'*(melo1 - melo2);
agree2 = comp2 < eps
comp3 = (mehi1 - mehi2)'*(mehi1 - mehi2);
agree3 = comp3 < eps

agree1 =

  logical

   1


agree2 =

  logical

   1


agree3 =

  logical

   1

The generated MEX function produces the same predictions as predict.

References

[1] Dobson, A. J. An Introduction to Generalized Linear Models. New York: Chapman & Hall, 1990.

[2] McCullagh, P., and J. A. Nelder. Generalized Linear Models. New York: Chapman & Hall, 1990.

[3] Collett, D. Modeling Binary Data. New York: Chapman & Hall, 2002.

Extended Capabilities

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Version History

Introduced before R2006a

See Also

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