Stata 15 help for manova_postestimation

[MV] manova postestimation -- Postestimation tools for manova

Postestimation commands

The following postestimation commands are of special interest after manova:

Command Description ------------------------------------------------------------------------- manovatest multivariate tests after manova screeplot plot eigenvalues -------------------------------------------------------------------------

The following standard postestimation commands are also available:

Command Description ------------------------------------------------------------------------- contrast contrasts and ANOVA-style joint tests of estimates estat summarize summary statistics for the estimation sample estat vce variance-covariance matrix of the estimators (VCE) estimates cataloging estimation results lincom point estimates, standard errors, testing, and inference for linear combinations of coefficients margins marginal means, predictive margins, marginal effects, and average marginal effects marginsplot graph the results from margins (profile plots, interaction plots, etc.) nlcom point estimates, standard errors, testing, and inference for nonlinear combinations of coefficients predict predictions, residuals, and standard errors predictnl point estimates, standard errors, testing, and inference for generalized predictions pwcompare pairwise comparisons of estimates test Wald tests of simple and composite linear hypotheses testnl Wald tests of nonlinear hypotheses -------------------------------------------------------------------------

Syntax for predict

predict [type] newvar [if] [in] [, equation(eqno[, eqno]) statistic]

statistic Description ------------------------------------------------------------------------- Main xb xb, fitted values; the default stdp standard error of the fitted value residuals residuals difference difference between the linear predictions of two equations stddp standard error of the fitted values for differences ------------------------------------------------------------------------- These statistics are available both in and out of sample; type predict ... if e(sample) ... if wanted only for the estimation sample.

Menu for predict

Statistics > Postestimation

Description for predict

predict creates a new variable containing predictions such as fitted values, standard errors, residuals, and differences between the linear predictions.

Options for predict

+------+ ----+ Main +-------------------------------------------------------------

equation(eqno [, eqno]) specifies the equation to which you are referring.

equation() is filled in with one eqno for the xb, stdp, and residuals options. equation(#1) would mean that the calculation is to be made for the first equation (that is, for the first dependent variable), equation(#2) would mean the second, and so on. You could also refer to the equations by their names. equation(income) would refer to the equation named income and equation(hours), to the equation named hours.

If you do not specify equation(), results are the same as if you had specified equation(#1).

difference and stddp refer to between-equations concepts. To use these options, you must specify two equations, for example, equation(#1,#2) or equation(income,hours). When two equations must be specified, equation() is required. With equation(#1,#2), difference computes the prediction of equation(#1) minus the prediction of equation(#2).

xb, the default, calculates the fitted values--the prediction of xb for the specified equation.

stdp calculates the standard error of the prediction for the specified equation (the standard error of the estimated expected value or mean for the observation's covariate pattern). The standard error of the prediction is also referred to as the standard error of the fitted value.

residuals calculates the residuals.

difference calculates the difference between the linear predictions of two equations in the system.

stddp calculates the standard error of the difference in linear predictions (x_{1j}b - x_{2j}b) between equations 1 and 2.

For more information on using predict after multiple-equation estimation commands, see [R] predict.

Syntax for margins

margins [marginlist] [, options]

margins [marginlist] , predict(statistic ...) [predict(statistic ...) ...] [options]

statistic Description ------------------------------------------------------------------------- default linear predictions for each equation xb linear prediction for a specified equation difference difference between the linear predictions of two equations residuals not allowed with margins stdp not allowed with margins stddp not allowed with margins ------------------------------------------------------------------------- xb defaults to the first equation.

Statistics not allowed with margins are functions of stochastic quantities other than e(b).

For the full syntax, see [R] margins.

Menu for margins

Statistics > Postestimation

Description for margins

margins estimates margins of responses for linear predictions, fitted values, and differences between the linear predictions.

Syntax for manovatest

manovatest term [term ...] [/ term [term ...]] [, ytransform(matname)]

manovatest, test(matname) [ytransform(matname)]

manovatest , showorder

where term is a term from the termlist in the previously run manova.

Menu for manovatest

Statistics > Multivariate analysis > MANOVA, multivariate regression, and related > Multivariate tests after MANOVA

Description for manovatest

manovatest provides multivariate tests involving terms or linear combinations of the underlying design matrix from the most recently fit manova. The four multivariate test statistics are Wilks's lambda, Pillai's trace, Lawley-Hotelling trace, and Roy's largest root. The format of the output is similar to that shown by manova.

Options for manovatest

ytransform(matname) specifies a matrix for transforming the y variables (the depvarlist from manova) as part of the test. The multivariate tests are based on inv(A*E*A')*(A*H*A'). By default, A is the identity matrix. ytransform() is how you specify an A matrix to be used in the multivariate tests. Specifying ytransform() provides the same results as first transforming the y variables with Y*A', where Y is the matrix formed by binding the y variables by column and A is the matrix stored in matname; then performing the manova on the transformed y's; and finally running manovatest without ytransform().

The number of columns of matname must equal the number of variables in the depvarlist from manova. The number of rows must be less than or equal to the number of variables in the depvarlist from manova. matname should have columns in the same order as the depvarlist from manova. The column and row names of matname are ignored.

When ytransform() is specified, a listing of the transformations is presented before the table containing the multivariate tests. You should examine this table to verify that you have applied the transformation you desired.

test(matname) is required with the second syntax of manovatest. The rows of matname specify linear combinations of the underlying design matrix of the MANOVA that are to be jointly tested. The columns correspond to the underlying design matrix (including the constant if it has not been suppressed). The column and row names of matname are ignored.

A listing of the constraints imposed by the test() option is presented before the table containing the multivariate tests. You should examine this table to verify that you have applied the linear combinations you desired. Typing manovatest, showorder allows you to examine the ordering of the columns for the design matrix from the MANOVA.

showorder causes manovatest to list the definition of each column in the design matrix. showorder is not allowed with any other option or when terms are specified.

Syntax for test

In addition to the standard syntax of test, test after manova also allows the following.

test, test(matname) [mtest[(opt)] matvlc(matname)] syntax A

test, showorder syntax B

syntax A test expression involving the coefficients of the underlying multivariate regression model; you provide information as a matrix syntax B show underlying order of design matrix, which is useful when constructing the matname argument of the test() option

Menu for test

Statistics > Multivariate analysis > MANOVA, multivariate regression, and related > Wald test after MANOVA

Description for test

In addition to the standard syntax of test, test after manova has two additionally allowed syntaxes; see below. test performs Wald tests of expressions involving the coefficients of the underlying regression model. Simple and composite linear hypotheses are possible.

Options for test

+------+ ----+ Main +-------------------------------------------------------------

test(matname) is required with syntax A of test. The rows of matname specify linear combinations of the underlying design matrix of the MANOVA that are to be jointly tested. The columns correspond to the underlying design matrix (including the constant if it has not been suppressed). The column and row names of matname are ignored.

A listing of the constraints imposed by the test() option is presented before the table containing the tests. You should examine this table to verify that you have applied the linear combinations you desired. Typing test, showorder allows you to examine the ordering of the columns for the design matrix from the MANOVA.

matname should have as many columns as the number of dependent variables times the number of columns in the basic design matrix. The design matrix is repeated for each dependent variable.

showorder causes test to list the definition of each column in the design matrix. showorder is not allowed with any other option.

+---------+ ----+ Options +----------------------------------------------------------

mtest[(opt)] specifies that tests be performed for each condition separately. opt specifies the method for adjusting p-values for multiple testing. Valid values for opt are

bonferroni Bonferroni's method holm Holm's method sidak Sidak's method noadjust no adjustment is to be made

Specifying mtest without an argument is equivalent to specifying mtest(noadjust).

The following option is available with test after manova but is not shown in the dialog box:

matvlc(matname), a programmer's option, saves the variance-covariance matrix of the linear combinations involved in the suite of tests. For the test of H_0: L*b = c, what is returned in matname is L*V*L', where V is the estimated variance-covariance matrix of b.

Examples

--------------------------------------------------------------------------- Setup . webuse metabolic . manova y1 y2 = group

Test group 1 versus groups 2, 3, and 4 . manovatest, showorder . matrix c1 = (3,-1,-1,-1,0) . manovatest, test(c1)

--------------------------------------------------------------------------- Setup . webuse sorghum . manova time1 time2 time3 time4 time5 = variety block . matrix m1 = J(1,5,1) . matrix m2 = (1,-1,0,0,0 \ 1,0,-1,0,0 \ 1,0,0,-1,0 \ 1,0,0,0,-1) . manovatest, showorder . mat c1 = (1,-1,0,0,0,0,0,0,0,0\1,0,-1,0,0,0,0,0,0,0\1,0,0,-1,0,0,0,0,0,0) . matrix c2 = (.25,.25,.25,.25,.2,.2,.2,.2,.2,1)

Test for equal variety marginal means . manovatest, test(c1) ytransform(m1)

Test for equal time marginal means . manovatest, test(c2) ytransform(m2)

Test variety by time interaction . manovatest, test(c1) ytransform(m2)

--------------------------------------------------------------------------- Setup . webuse biochemical . manova y1 y2 y3 = group c.x1 c.x2

Test that the continuous covariates are jointly equal to zero . manovatest c.x1 c.x2 -------------------------------------------------------------------------- Setup . webuse biochemical . manova y1 y2 y3 = group c.x1 c.x2 group#c.x1 group#c.x2

Test that the continuous covariates are jointly equal to zero across groups . manovatest group#c.x1 group#c.x2 ---------------------------------------------------------------------------

Setup . webuse jaw . manova y1 y2 y3 = gender fracture gender#fracture

Compute the predicted mean (marginal mean), standard error, z statistic, p-value, and confidence interval of y1 for each combination of fracture and gender . margins gender#fracture, predict(equation(y1))

Contrast women with men for every fracture type and every dependent variable . contrast gender@fracture#_eqns, mcompare(scheffe) ---------------------------------------------------------------------------

Stored results

manovatest stores the following in r():

Scalars r(df) hypothesis degrees of freedom r(df_r) residual degrees of freedom

Matrices r(H) hypothesis SSCP matrix r(E) residual-error SSCP matrix r(stat) multivariate statistics r(eigvals) eigenvalues of E^-1H r(aux) s, m, and n values

test after manova stores the following in r():

Scalars r(p) two-sided p-value r(F) F statistic r(df) hypothesis degrees of freedom r(df_r) residual degrees of freedom r(drop) 0 if no constraints dropped, 1 otherwise r(dropped_#) index of #th constraint dropped

Macros r(mtmethod) method of adjustment for multiple testing

Matrices r(mtest) multiple test results


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