Class: GeneralizedLinearModel

Add terms to generalized linear model


mdl1 = addTerms(mdl,terms)


mdl1 = addTerms(mdl,terms) returns a generalized linear model the same as mdl but with additional terms.

Input Arguments


Generalized linear model, as constructed by fitglm or stepwiseglm.


Terms to add to the regression model mdl, specified as one of the following:

  • A character vector or string scalar formula in Wilkinson Notation representing one or more terms. The variable names in the formula must be valid MATLAB® identifiers.

  • Terms matrix T of size t-by-p, where t is the number of terms and p is the number of predictor variables in mdl. The value of T(i,j) is the exponent of variable j in term i.

    For example, suppose mdl has three variables A, B, and C in that order. Each row of T represents one term:

    • [0 0 0] — Constant term or intercept

    • [0 1 0]B; equivalently, A^0 * B^1 * C^0

    • [1 0 1]A*C

    • [2 0 0]A^2

    • [0 1 2]B*(C^2)

Output Arguments


Generalized linear model, the same as mdl but with additional terms given in terms. You can set mdl1 equal to mdl to overwrite mdl.


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Create a model using just one predictor, then add a second.

Generate artificial data for the model, Poisson random numbers with two underlying predictors X(1) and X(2).

rng default % for reproducibility
rndvars = randn(100,2);
X = [2+rndvars(:,1),rndvars(:,2)];
mu = exp(1 + X*[1;2]);
y = poissrnd(mu);

Create a generalized linear regression model of Poisson data. Use just the first predictor in the model.

mdl = fitglm(X,y,...
    'y ~ x1','distr','poisson')
mdl = 
Generalized linear regression model:
    log(y) ~ 1 + x1
    Distribution = Poisson

Estimated Coefficients:
                   Estimate       SE        tStat     pValue
                   ________    _________    ______    ______

    (Intercept)     2.7784      0.014043    197.85      0   
    x1              1.1732     0.0033653     348.6      0   

100 observations, 98 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 1.25e+05, p-value = 0

Add the second predictor to the model.

mdl1 = addTerms(mdl,'x2')
mdl1 = 
Generalized linear regression model:
    log(y) ~ 1 + x1 + x2
    Distribution = Poisson

Estimated Coefficients:
                   Estimate       SE        tStat     pValue
                   ________    _________    ______    ______

    (Intercept)     1.0405      0.022122    47.034      0   
    x1              0.9968      0.003362    296.49      0   
    x2               1.987     0.0063433    313.24      0   

100 observations, 97 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 2.95e+05, p-value = 0

More About

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  • addTerms treats a categorical predictor as follows:

    • A model with a categorical predictor that has L levels (categories) includes L – 1 indicator variables. The model uses the first category as a reference level, so it does not include the indicator variable for the reference level. If the data type of the categorical predictor is categorical, then you can check the order of categories by using categories and reorder the categories by using reordercats to customize the reference level.

    • addTerms treats the group of L – 1 indicator variables as a single variable. If you want to treat the indicator variables as distinct predictor variables, create indicator variables manually by using dummyvar. Then use the indicator variables, except the one corresponding to the reference level of the categorical variable, when you fit a model. For the categorical predictor X, if you specify all columns of dummyvar(X) and an intercept term as predictors, then the design matrix becomes rank deficient.

    • Interaction terms between a continuous predictor and a categorical predictor with L levels consist of the element-wise product of the L – 1 indicator variables with the continuous predictor.

    • Interaction terms between two categorical predictors with L and M levels consist of the (L – 1)*(M – 1) indicator variables to include all possible combinations of the two categorical predictor levels.

    • You cannot specify higher-order terms for a categorical predictor because the square of an indicator is equal to itself.


step adds or removes terms from a model using a greedy one-step algorithm.


[1] Wilkinson, G. N., and C. E. Rogers. Symbolic description of factorial models for analysis of variance. J. Royal Statistics Society 22, pp. 392–399, 1973.