removeTerms

Class: GeneralizedLinearModel

Remove terms from generalized linear model

Syntax

mdl1 = removeTerms(mdl,terms)


Description

mdl1 = removeTerms(mdl,terms) returns a linear model the same as mdl but with fewer terms.

Input Arguments

mdl

Generalized linear model, as constructed by fitglm or stepwiseglm.

terms

Terms to remove from 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

mdl1	Generalized linear model, the same as mdl but without the terms given in terms. You can set mdl1 equal to mdl to overwrite mdl.

Examples

Remove a Term from a Generalized Linear Regression Model

This example makes a model using two predictors, then removes one.

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.

mdl = fitglm(X,y,'y ~ x1 + x2','distr','poisson')

mdl = 
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

Remove the second predictor from the model.

mdl1 = removeTerms(mdl,'x2')

mdl1 = 
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

More About

Wilkinson Notation

Wilkinson notation describes the terms present in a model. The notation relates to the terms present in a model, not to the multipliers (coefficients) of those terms.

Wilkinson notation uses these symbols:

• + means include the next variable.

• – means do not include the next variable.

• : defines an interaction, which is a product of terms.

• * defines an interaction and all lower-order terms.

• ^ raises the predictor to a power, exactly as in * repeated, so ^ includes lower-order terms as well.

• () groups terms.

This table shows typical examples of Wilkinson notation.

Wilkinson Notation	Term in Standard Notation
1	Constant (intercept) term
A^k, where k is a positive integer	A, A2, ..., Ak
A + B	A, B
A*B	A, B, A*B
A:B	A*B only
–B	Do not include B
A*B + C	A, B, C, A*B
A + B + C + A:B	A, B, C, A*B
A*B*C – A:B:C	A, B, C, A*B, A*C, B*C
A*(B + C)	A, B, C, A*B, A*C

Statistics and Machine Learning Toolbox™ notation always includes a constant term unless you explicitly remove the term using –1.

For more details, see Wilkinson Notation.

For details, see Wilkinson and Rogers [1].

Algorithms

• removeTerms 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.

  • removeTerms 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.

Alternatives

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

References

[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.