CompactLinearModel

Compact linear regression model

Description

CompactLinearModel is a compact version of a full linear regression model object LinearModel. Because a compact model does not store the input data used to fit the model or information related to the fitting process, a CompactLinearModel object consumes less memory than a LinearModel object. You can still use a compact model to predict responses using new input data, but some LinearModel object functions do not work with a compact model.

Creation

Create a CompactLinearModel model from a full, trained LinearModel model by using compact.

Properties

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Coefficient Estimates

Covariance matrix of coefficient estimates, specified as a p-by-p matrix of numeric values. p is the number of coefficients in the fitted model.

For details, see Coefficient Standard Errors and Confidence Intervals.

Data Types: single | double

Coefficient names, specified as a cell array of character vectors, each containing the name of the corresponding term.

Data Types: cell

Coefficient values, specified as a table. Coefficients contains one row for each coefficient and these columns:

• Estimate — Estimated coefficient value

• SE — Standard error of the estimate

• tStatt-statistic for a test that the coefficient is zero

• pValuep-value for the t-statistic

Use anova (only for a linear regression model) or coefTest to perform other tests on the coefficients. Use coefCI to find the confidence intervals of the coefficient estimates.

To obtain any of these columns as a vector, index into the property using dot notation. For example, obtain the estimated coefficient vector in the model mdl:

beta = mdl.Coefficients.Estimate

Data Types: table

Number of model coefficients, specified as a positive integer. NumCoefficients includes coefficients that are set to zero when the model terms are rank deficient.

Data Types: double

Number of estimated coefficients in the model, specified as a positive integer. NumEstimatedCoefficients does not include coefficients that are set to zero when the model terms are rank deficient. NumEstimatedCoefficients is the degrees of freedom for regression.

Data Types: double

Summary Statistics

Degrees of freedom for the error (residuals), equal to the number of observations minus the number of estimated coefficients, specified as a positive integer.

Data Types: double

Loglikelihood of response values, specified as a numeric value, based on the assumption that each response value follows a normal distribution. The mean of the normal distribution is the fitted (predicted) response value, and the variance is the MSE.

Data Types: single | double

Criterion for model comparison, specified as a structure with these fields:

• AIC — Akaike information criterion. AIC = –2*logL + 2*m, where logL is the loglikelihood and m is the number of estimated parameters.

• AICc — Akaike information criterion corrected for the sample size. AICc = AIC + (2*m*(m + 1))/(n – m – 1), where n is the number of observations.

• BIC — Bayesian information criterion. BIC = –2*logL + m*log(n).

• CAIC — Consistent Akaike information criterion. CAIC = –2*logL + m*(log(n) + 1).

Information criteria are model selection tools that you can use to compare multiple models fit to the same data. These criteria are likelihood-based measures of model fit that include a penalty for complexity (specifically, the number of parameters). Different information criteria are distinguished by the form of the penalty.

When you compare multiple models, the model with the lowest information criterion value is the best-fitting model. The best-fitting model can vary depending on the criterion used for model comparison.

To obtain any of the criterion values as a scalar, index into the property using dot notation. For example, obtain the AIC value aic in the model mdl:

aic = mdl.ModelCriterion.AIC

Data Types: struct

Mean squared error (residuals), specified as a numeric value.

MSE = SSE / DFE,

where MSE is the mean squared error, SSE is the sum of squared errors, and DFE is the degrees of freedom.

Data Types: single | double

Root mean squared error (residuals), specified as a numeric value.

RMSE = sqrt(MSE),

where RMSE is the root mean squared error and MSE is the mean squared error.

Data Types: single | double

R-squared value for the model, specified as a structure with two fields:

• Ordinary — Ordinary (unadjusted) R-squared

The R-squared value is the proportion of the total sum of squares explained by the model. The ordinary R-squared value relates to the SSR and SST properties:

Rsquared = SSR/SST,

where SST is the total sum of squares, and SSR is the regression sum of squares.

For details, see Coefficient of Determination (R-Squared).

To obtain either of these values as a scalar, index into the property using dot notation. For example, obtain the adjusted R-squared value in the model mdl:

Data Types: struct

Sum of squared errors (residuals), specified as a numeric value.

The Pythagorean theorem implies

SST = SSE + SSR,

where SST is the total sum of squares, SSE is the sum of squared errors, and SSR is the regression sum of squares.

Data Types: single | double

Regression sum of squares, specified as a numeric value. The regression sum of squares is equal to the sum of squared deviations of the fitted values from their mean.

The Pythagorean theorem implies

SST = SSE + SSR,

where SST is the total sum of squares, SSE is the sum of squared errors, and SSR is the regression sum of squares.

Data Types: single | double

Total sum of squares, specified as a numeric value. The total sum of squares is equal to the sum of squared deviations of the response vector y from the mean(y).

The Pythagorean theorem implies

SST = SSE + SSR,

where SST is the total sum of squares, SSE is the sum of squared errors, and SSR is the regression sum of squares.

Data Types: single | double

Fitting Method

Robust fit information, specified as a structure with the fields described in this table.

FieldDescription
WgtFunRobust weighting function, such as 'bisquare' (see 'RobustOpts')
TuneTuning constant. This field is empty ([]) if WgtFun is 'ols' or if WgtFun is a function handle for a custom weight function with the default tuning constant 1.
WeightsVector of weights used in the final iteration of robust fit. This field is empty for a CompactLinearModel object.

This structure is empty unless you fit the model using robust regression.

Data Types: struct

Input Data

Model information, specified as a LinearFormula object.

Display the formula of the fitted model mdl using dot notation:

mdl.Formula

Number of observations the fitting function used in fitting, specified as a positive integer. NumObservations is the number of observations supplied in the original table, dataset, or matrix, minus any excluded rows (set with the 'Exclude' name-value pair argument) or rows with missing values.

Data Types: double

Number of predictor variables used to fit the model, specified as a positive integer.

Data Types: double

Number of variables in the input data, specified as a positive integer. NumVariables is the number of variables in the original table or dataset, or the total number of columns in the predictor matrix and response vector.

NumVariables also includes any variables that are not used to fit the model as predictors or as the response.

Data Types: double

Names of predictors used to fit the model, specified as a cell array of character vectors.

Data Types: cell

Response variable name, specified as a character vector.

Data Types: char

Information about variables contained in Variables, specified as a table with one row for each variable and the columns described in this table.

ColumnDescription
ClassVariable class, specified as a cell array of character vectors, such as 'double' and 'categorical'
Range

Variable range, specified as a cell array of vectors

• Continuous variable — Two-element vector [min,max], the minimum and maximum values

• Categorical variable — Vector of distinct variable values

InModelIndicator of which variables are in the fitted model, specified as a logical vector. The value is true if the model includes the variable.
IsCategoricalIndicator of categorical variables, specified as a logical vector. The value is true if the variable is categorical.

VariableInfo also includes any variables that are not used to fit the model as predictors or as the response.

Data Types: table

Names of variables, specified as a cell array of character vectors.

• If the fit is based on a table or dataset, this property provides the names of the variables in the table or dataset.

• If the fit is based on a predictor matrix and response vector, VariableNames contains the values specified by the 'VarNames' name-value pair argument of the fitting method. The default value of 'VarNames' is {'x1','x2',...,'xn','y'}.

VariableNames also includes any variables that are not used to fit the model as predictors or as the response.

Data Types: cell

Object Functions

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 feval Predict responses of linear regression model using one input for each predictor predict Predict responses of linear regression model random Simulate responses with random noise for linear regression model
 anova Analysis of variance for linear regression model coefCI Confidence intervals of coefficient estimates of linear regression model coefTest Linear hypothesis test on linear regression model coefficients partialDependence Compute partial dependence
 plotEffects Plot main effects of predictors in linear regression model plotInteraction Plot interaction effects of two predictors in linear regression model plotPartialDependence Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots plotSlice Plot of slices through fitted linear regression surface
 gather Gather properties of Statistics and Machine Learning Toolbox object from GPU

Examples

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Fit a linear regression model to data and reduce the size of a full, fitted linear regression model by discarding the sample data and some information related to the fitting process.

Load the largedata4reg data set, which contains 15,000 observations and 45 predictor variables.

Fit a linear regression model to the data.

mdl = fitlm(X,Y);

Compact the model.

compactMdl = compact(mdl);

The compact model discards the original sample data and some information related to the fitting process.

Compare the size of the full model mdl and the compact model compactMdl.

vars = whos('compactMdl','mdl');
[vars(1).bytes,vars(2).bytes]
ans = 1×2

81537    11408528

The compact model consumes less memory than the full model.