# lsdvFit¶

## Purpose¶

Estimates coefficients of a regression model with autoregressive errors of any specified order.

## Format¶

lout1 = lsdvFit(y, x, series_length, n_lags[, lsc])
lout1 = lsdvFit(dataset, formula, series_length, n_lags[, lsc])
Parameters
• y (Nx1 vector) – data.

• x (Nxk vector) – independent data.

• dataset (string) – name of data set or null string.

• 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’;

• series_length (scalar) – number of time periods for each case or instance.

• num_lags (scalar) – number of lagged values of the dependent variable.

• lsc (struct) –

Optional input, an instance of a lsdvmtControl structure. The following members of lsc are referenced within this routine:

 lsc.Constrain scalar, if nonzero constraints will be applied to the autoregression coefficients. Default = 1. lsc.scale scalar, if nonzero, data are scaled. lsc.output scalar, determines the output to be printed. lsc.title string, title to be printed at top of header.

Returns

out (struct) –

An instance of an lsdvOutstructure. The following members of out are referenced within this routine:

 autoCoefficients Jx1 vector, uncorrected autoregression coefficients. regCoefficients Kx1 vector, uncorrected regression coefficients. autoCoefficientsCorr Jx1 vector, bias corrected autoregression coefficients. regCoefficientsCorr Kx1 vector, bias corrected regression coefficients. autoStderrs Jx1 vector, autoregression coefficient standard errors. regStderrs Kx1 vector, regression coefficient standard errors. covPar KxK matrix, covariance matrix of parameters SSresidual scalar, residual sums of squares. SStotal scalar, total sums of squares. SSexplained scalar, explained sums of squares. SSpooledResidual scalar, pooled residual sums of squares. biasCorr K+Jx1 vector, bias corrections. lagrange Jx2 matrix, Lagrangeans for constraints. numCases scalar, number of cases. numMissing scalar, number of observations with missing data. numDF scalar, number of degrees of freedom. numObservations scalar, number of observations. numParameters scalar, number of parameters. numPeriods scalar, number of periods in time series.

## Examples¶

### Dataset and formula¶

new;
library tsmt;

// Declare lsdvmt control structure
struct lsdvmtControl c0;
c0 = lsdvmtControlCreate();

// Turn screen output on
c0.output = 1;

// Scale data before running
c0.scale = 0;

// Declare output structure
struct lsdvmtOut out;

// Call lsdvmt function
out = lsdvFit(getGAUSSHome() $+ "pkgs/tsmt/examples/lsdv.dat", "Y~X1+X2+X3", 50, 2, c0);  ### Data matrices¶ new; library tsmt; //Load data data = loadd( getGAUSSHome()$+ "pkgs/tsmt/examples/lsdv.dat");

//Dependent variable
y = data[., 1];

//Independent variable
x = data[., 2:4];

//Declare lsdvmt control structure
struct lsdvmtControl c0;
c0 = lsdvmtControlCreate();

//Turn screen output on
c0.output = 1;

//Scale data before running
c0.scale = 0;

//Declare output structure
struct lsdvmtOut out;

//Call lsdvmt function
out = lsdvFit(y, x, 50, 2, c0);


## Remarks¶

The data must be contained in a GAUSS dataset cross-sectional unit by cross-sectional unit, with one variable containing an index for the units. From each cross-sectional unit all observations must be grouped together. For example, for the first cross-sectional unit there may be 10 rows in the dataset, for the second cross-sectional unit there may be another 10 rows, and so on. Each row in the dataset contains measurements on the endogenous and exogenous variables measured for each observation along with the index identifying the cross-sectional unit.

The index variable must be a series of integers. While all observations for each cross-sectional unit must be grouped together, they do not have to be sorted according to the index.

tsmt

lsdvmt.src