quantileFit

Purpose

Perform linear quantile regression.

Format

qOut = quantileFit(y, x[, tau, w, qCtl])
qOut = quantileFit(dataset, formula[, tau, w, qCtl])
qOut = quantileFit(dataframe, formula[, tau, w, qCtl])
Parameters
  • y (Nx1 vector) – dependent variable.

  • x (NxK matrix or sparse matrix or N-dimensional array) – independent variables.

  • dataset (string) – name of dataset.

  • formula (string) –

    formula string of the model.

    E.g "y ~ X1 + X2", ‘y’ is the name of dependent variable, ‘X1’ and ‘X2’ are names of independent variables;

    E.g "y ~ .", ‘.’ means including all variables except dependent variable ‘y’;

    E.g "y ~ -1 + X1 + X2", ‘-1’ means no intercept model.

  • tau (Mx1 vector) – Optional argument, quantile levels. Default = { 0.05, 0.5, 0.95 };

  • w (Nx1 vector) – Optional argument, containing weights. Default = uniform weights.

  • qCtl (struct) –

    Optional argument, instance of the qfitControl structure containing the following members:

    qCtl.bandwidth

    scalar, the multiplicative factor of the bandwidth. Default = 1.

    qCtl.varnames

    Kx1 string array, variable names. Default = {"X1", "X2", ..., "XK"}. The name for the constant will be added automatically if it is included in the model.

    qCtl.verbose

    scalar, print results Default = 1.

    1

    Printing on.

    0

    No printing.

    qCtl.const

    scalar, include constant in regression. Default = 1.

    1

    a constant term will be added.

    0

    no constant term will be added.

    qCtl.vce_method

    scalar, method to use for calculating the asymptotic covariance matrix. Default = 1.

    1

    IID errors.

    2

    heteroskedasticity robust standard errors.

    qCtl.bw_method

    scalar, method to use for calculating the bandwidth for the asymptotic covariance matrix computation. Default = 1.

    1

    Hall-Sheather bandwidth.

    2

    Bofinger bandwidth.

    3

    Chamberlain bandwidth.

    qCtl.vce_kernel

    scalar,kernel to use for calculating the asymptotic covariance matrix computation. Default = 1.

    1

    Normal(Gaussian).

    2

    Epanechnikov.

    3

    Biweight.

    4

    Parzen.

    5

    Cosine.

    qCtl.bootstrap

    scalar, number of iterations for bootstrap standard errors and confidence intervals. Default = 0, for no bootstrap.

    qCtl.alpha

    scalar, alpha values for bootstrap confidence intervals.

Returns

qOut (struct) –

instance of qfitOut struct structure:

qOut.beta

KxM matrix, quantile parameter estimates, with estimates for each tau stored in a separate column.

qOut.u_plus

NxM matrix, positive part of residuals.

qOut.u_minus

NxM matrix, negative part of residuals.

qOut.vce

array, with a KxK matrix estimated asymptotic covariance matrix stored on a separate plane for each tau specified.

qOut.vce_ci

array, with a Kx2 matrix containing lower and upper confidence intervals based on asymptotic covariance estimates stored on separate planes for each tau specified.

qOut.vce_se

matrix, with estimated asymptotic standard errors, stored in separate columns for each tau specified.

qOut.ci

array, with a Kx2 matrix containing bootstrapped lower and upper confidence intervals stored on separate planes for each tau specified.

qOut.se

matrix, with bootstrapped standard errors, stored in a separate column for each tau specified.

qOut.t

KxM matrix, with estimate t-values based on asymptotic standard errors. Estimates for each tau are stored in a separate column.

qOut.pvt

KxM matrix, with p-values for estimated t-values. Estimates for each tau are stored in a separate column.

qOut.number_obs

Scalar, number of observations used in estimation.

qOut.number_missing

Scalar, number of missing values eliminated from original data.

qOut.df_residuals

Scalar, residual degrees of freedom.

qOut.df_model

Scalar, model degrees of freedom.

qOut.h

Vector, bandwidth used in asymptotic variance estimation. Values for each tau are stored in separate columns.

qOut.sparsity

Vector, sparsity used in asymptotic variance estimation. Values for each tau are stored in separate columns.

Examples

new;
cls;

// Set random number generator seed for
// repeatable random numbers
rndseed 4893;

N = 1000;
x = 10*rndu(N, 1) - 5;
y = 5 + 2*X + rndn(rows(x), 1)*10;

// Set up tau for regression
tau = 0.05;

// Call quantileFit
struct qfitOut qOut;
qOut = quantileFit(Y, X, tau);

This produces the following output

 =====================================================================================
 Valid cases:                   1000                Dependent variable:              Y
 Missing cases:                    0                   Deletion method:           None
 Number variables:                 1                           DF model              1
 DF residuals                    998
 =====================================================================================

                    Name    Coeff.  Standard   t-value    P >|t|        lb        ub
                                       Error
-------------------------------------------------------------------------------------
Tau = 0.05

                CONSTANT  -11.6768    0.5542  -21.0713    0.0000  -12.7629  -10.5907
                      X1    1.6790    0.1885    8.9059    0.0000    1.3095    2.0485

Source

quantilefit.src

See also

Functions glm(), olsmt(), quantileFitLoc()