Stata 15 help for contrast

[R] contrast -- Contrasts and linear hypothesis tests after estimation

Syntax

contrast termlist [, options]

where termlist is a list of factor variables or interactions that appear in the current estimation results. The variables may be typed with or without contrast operators, and you may use any factor-variable syntax.

See the operators (op.) table below for the list of contrast operators.

options Description ------------------------------------------------------------------------- Main overall add a joint hypothesis test for all specified contrasts asobserved treat all factor variables as observed lincom treat user-defined contrasts as linear combinations

Equations equation(eqspec) perform contrasts in termlist for equation eqspec atequations perform contrasts in termlist within each equation

Advanced emptycells(empspec) treatment of empty cells for balanced factors noestimcheck suppress estimability checks

Reporting level(#) confidence level; default is level(95) mcompare(method) adjust for multiple comparisons; default is mcompare(noadjust) noeffects suppress table of individual contrasts cieffects show effects table with confidence intervals pveffects show effects table with p-values effects show effects table with confidence intervals and p-values nowald suppress table of Wald tests noatlevels report only the overall Wald test for terms that use the within @ or nested | operator nosvyadjust compute unadjusted Wald tests for survey results sort sort the individual contrast values in each term post post contrasts and their VCEs as estimation results display_options control column formats, row spacing, line width, and factor-variable labeling eform_option report exponentiated contrasts

df(#) use t distribution with # degrees of freedom for computing p-values and confidence intervals ------------------------------------------------------------------------- df(#) does not appear in the dialog box.

Term Description ------------------------------------------------------------------------- Main effects A joint test of the main effects of A r.A individual contrasts that decompose A using r. Interaction effects A#B joint test of the two-way interaction effects of A and B A#B#C joint test of the three-way interaction effects of A, B, and C r.A#g.B individual contrasts for each interaction of A and B defined by r. and g. Partial interaction effects r.A#B joint tests of interactions of A and B within each contrast defined by r.A A#r.B joint tests of interactions of A and B within each contrast defined by r.B Simple effects A@B joint tests of the effects of A within each level of B A@B#C joint tests of the effects of A within each combination of the levels of B and C r.A@B individual contrasts of A that decompose A@B using r. r.A@B#C individual contrasts of A that decompose A@B#C using r. Other conditional effects A#B@C joint tests of the interaction effects of A and B within each level of C A#B@C#D joint tests of the interaction effects of A and B within each combination of the levels of C and D r.A#g.B@C individual contrasts for each interaction of A and B that decompose A#B@C using r. and g.

Nested effects A|B joint tests of the effects of A nested in each level of B A|B#C joint tests of the effects of A nested in each combination of the levels of B and C A#B|C joint tests of the interaction effects of A and B nested in each level of C A#B|C#D joint tests of the interaction effects of A and B nested in each combination of the levels of C and D r.A|B individual contrasts of A that decompose A|B using r. r.A|B#C individual contrasts of A that decompose A|B#C using r. r.A#g.B|C individual contrasts for each interaction of A and B defined by r. and g. nested in each level of C Slope effects A#c.x joint test of the effects of A on the slopes of x A#c.x#c.y joint test of the effects of A on the slopes of the product (interaction) of x and y A#B#c.x joint test of the interaction effects of A and B on the slopes of x A#B#c.x#c.y joint test of the interaction effects of A and B on the slopes of the product (interaction) of x and y r.A#c.x individual contrasts of A's effects on the slopes of x using r. Denominators .../term2 use term2 as the denominator in the F tests of the preceding terms .../ use the residual as the denominator in the F tests of the preceding terms (the default if no other /s are specified ------------------------------------------------------------------------- A, B, C, and D represent any factor variable in the current estimation results. x and y represent any continuous variable in the current estimation results. r. and g. represent any contrast operator. See the table below. c. specifies that a variable be treated as continuous; see fvvarlist. Operators are allowed on any factor variable that does not appear to the right of @ or |. Operators decompose the effects of the associated factor variable into one-degree-of-freedom effects (contrasts). Higher-level interactions are allowed anywhere an interaction operator (#) appears in the table. Time-series operators are allowed if they were used in the estimation. _eqns designates the equations in manova, mlogit, mprobit, and mvreg and can be specified anywhere a factor variable appears. / is allowed only after anova, cnsreg, manova, mvreg, or regress.

operators (op.) Description ------------------------------------------------------------------------- r. differences from the reference (base) level; the default a. differences from the next level (adjacent contrasts) ar. differences from the previous level (reverse adjacent contrasts)

As-balanced operators g. differences from the balanced grand mean h. differences from the balanced mean of subsequent levels (Helmert contrasts) j. differences from the balanced mean of previous levels (reverse Helmert contrasts) p. orthogonal polynomial in the level values q. orthogonal polynomial in the level sequence

As-observed operators gw. differences from the observation-weighted grand mean hw. differences from the observation-weighted mean of subsequent levels jw. differences from the observation-weighted mean of previous levels pw. observation-weighted orthogonal polynomial in the level values qw. observation-weighted orthogonal polynomial in the level sequence ------------------------------------------------------------------------- One or more individual contrasts may be selected by using the op#. or op( numlist). syntax. For example, a3.A selects the adjacent contrast for level 3 of A, and p(1/2).B selects the linear and quadratic effects of B. Also see Orthogonal polynomial contrasts and Beyond linear models in [R] contrast.

Custom contrasts Description ------------------------------------------------------------------------- {A numlist} user-defined contrast on the levels of factor A {A#B numlist} user-defined contrast on the levels of interaction between A and B ------------------------------------------------------------------------- Custom contrasts may be part of a term, such as {A numlist}#B, {A numlist}@B, {A numlist}|B, {A#B numlist}, and {A numlist}#{B numlist}. The same is true of higher-order custom contrasts, such as {A#B numlist}@C, {A#B numlist}#r.C, and {A#B numlist}#c.x. Higher-order interactions with at most eight factor variables are allowed with custom contrasts.

method Description ------------------------------------------------------------------------- noadjust do not adjust for multiple comparisons; the default bonferroni [adjustall] Bonferroni's method; adjust across all terms sidak [adjustall] Sidak's method; adjust across all terms scheffe Scheffe's method -------------------------------------------------------------------------

Menu

Statistics > Postestimation

Description

contrast tests linear hypotheses and forms contrasts involving factor variables and their interactions from the most recently fit model. The tests include ANOVA-style tests of main effects, simple effects, interactions, and nested effects. contrast can use named contrasts to decompose these effects into comparisons against reference categories, comparisons of adjacent levels, comparisons against the grand mean, orthogonal polynomials, and such. Custom contrasts may also be specified.

contrast can be used with svy estimation results; see [SVY] svy postestimation.

Contrasts can also be computed for margins of linear and nonlinear responses; see [R] margins, contrast.

Options

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

overall specifies that a joint hypothesis test over all terms be performed.

asobserved specifies that factor covariates be evaluated using the cell frequencies observed in the estimation sample. The default is to treat all factor covariates as though there were an equal number of observations in each level.

lincom specifies that user-defined contrasts be treated as linear combinations. The default is to require that all user-defined contrasts sum to zero. (Summing to zero is part of the definition of a contrast.)

+-----------+ ----+ Equations +--------------------------------------------------------

equation(eqspec) specifies the equation from which contrasts are to be computed. The default is to compute contrasts from the first equation.

atequations specifies that the contrasts be computed within each equation.

+----------+ ----+ Advanced +---------------------------------------------------------

emptycells(empspec) specifies how empty cells are handled in interactions involving factor variables that are being treated as balanced.

emptycells(strict) is the default; it specifies that contrasts involving empty cells be treated as not estimable.

emptycells(reweight) specifies that the effects of the observed cells be increased to accommodate any missing cells. This makes the contrast estimable but changes its interpretation.

noestimcheck specifies that contrast not check for estimability. By default, the requested contrasts are checked and those found not estimable are reported as such. Nonestimability is usually caused by empty cells. If noestimcheck is specified, estimates are computed in the usual way and reported even though the resulting estimates are manipulable, which is to say they can differ across equivalent models having different parameterizations.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#) specifies the confidence level, as a percentage, for confidence intervals. The default is level(95) or as set by set level.

mcompare(method) specifies the method for computing p-values and confidence intervals that account for multiple comparisons within a factor-variable term.

Most methods adjust the comparisonwise error rate, alpha_c, to achieve a prespecified experimentwise error rate, alpha_e.

mcompare(noadjust) is the default; it specifies no adjustment.

alpha_c = alpha_e

mcompare(bonferroni) adjusts the comparisonwise error rate based on the upper limit of the Bonferroni inequality

alpha_e <= m * alpha_c

where m is the number of comparisons within the term.

The adjusted comparisonwise error rate is

alpha_c = alpha_e/m

mcompare(sidak) adjusts the comparisonwise error rate based on the upper limit of the probability inequality

alpha_e <= 1 - (1 - alpha_c)^m

where m is the number of comparisons within the term.

The adjusted comparisonwise error rate is

alpha_c = 1 - (1 - alpha_e)^(1/m)

This adjustment is exact when the m comparisons are independent.

mcompare(scheffe) controls the experimentwise error rate using the F or chi-squared distribution with degrees of freedom equal to the rank of the term.

mcompare(method adjustall) specifies that the multiple-comparison adjustments count all comparisons across all terms rather than performing multiple comparisons term by term. This leads to more conservative adjustments when multiple variables or terms are specified in marginslist. This option is compatible only with the bonferroni and sidak methods.

noeffects suppresses the table of individual contrasts with confidence intervals. This table is produced by default when the mcompare() option is specified or when a term in termlist implies all individual contrasts.

cieffects specifies that a table containing a confidence interval for each individual contrast be reported.

pveffects specifies that a table containing a p-value for each individual contrast be reported.

effects specifies that a single table containing a confidence interval and p-value for each individual contrast be reported.

nowald suppresses the table of Wald tests.

noatlevels indicates that only the overall Wald test be reported for each term containing within or nested (@ or |) operators.

nosvyadjust is for use with svy estimation commands. It specifies that the Wald test be carried out without the default adjustment for the design degrees of freedom. That is to say the test is carried out as W/k ~ F(k,d) rather than as (d-k+1)W/(kd) ~ F(k,d-k+1), where k is the dimension of the test and d is the total number of sampled PSUs minus the total number of strata.

sort specifies that the table of individual contrasts be sorted by the contrast values within each term.

post causes contrast to behave like a Stata estimation (e-class) command. contrast posts the vector of estimated contrasts along with the estimated variance-covariance matrix to e(), so you can treat the estimated contrasts just as you would results from any other estimation command. For example, you could use test to perform simultaneous tests of hypotheses on the contrasts, or you could use lincom to create linear combinations.

display_options: vsquish, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch.

vsquish specifies that the blank space separating factor-variable terms or time-series-operated variables from other variables in the model be suppressed.

nofvlabel displays factor-variable level values rather than attached value labels. This option overrides the fvlabel setting; see [R] set showbaselevels.

fvwrap(#) specifies how many lines to allow when long value labels must be wrapped. Labels requiring more than # lines are truncated. This option overrides the fvwrap setting; see [R] set showbaselevels.

fvwrapon(style) specifies whether value labels that wrap will break at word boundaries or break based on available space.

fvwrapon(word), the default, specifies that value labels break at word boundaries.

fvwrapon(width) specifies that value labels break based on available space.

This option overrides the fvwrapon setting; see [R] set showbaselevels.

cformat(%fmt) specifies how to format contrasts, standard errors, and confidence limits in the table of estimated contrasts.

pformat(%fmt) specifies how to format p-values in the table of estimated contrasts.

sformat(%fmt) specifies how to format test statistics in the table of estimated contrasts.

nolstretch specifies that the width of the table of estimated contrasts not be automatically widened to accommodate longer variable names. The default, lstretch, is to automatically widen the table of estimated contrasts up to the width of the Results window. To change the default, use set lstretch off. nolstretch is not shown in the dialog box.

eform_option specifies that the contrasts table be displayed in exponentiated form. exp(contrast) is displayed rather than contrast. Standard errors and confidence intervals are also transformed. See [R] eform_option for the list of available options.

The following option is available with contrast but is not shown in the dialog box:

df(#) specifies that the t distribution with # degrees of freedom be used for computing p-values and confidence intervals. The default is to use e(df_r) degrees of freedom or the standard normal distribution if e(df_r) is missing.

Examples

--------------------------------------------------------------------------- Setup for one-way model . webuse cholesterol . regress chol i.agegrp

Test that the cell means are the same for all age groups, that is, test the main effects of age group . contrast agegrp

Reference category contrasts . contrast r.agegrp

Reverse adjacent contrasts . contrast ar.agegrp

Orthogonal polynomial contrasts . contrast p.agegrp

Setup for one-way model . anova chol i.race

Grand mean contrasts, adjusting p-values for multiple comparisons using Bonferroni's adjustment . contrast g.race, mcompare(bonferroni)

User-defined contrasts for reference category effects, testing that the cell mean of category 1 is equal to the cell mean of category 2 and that the cell mean of category 1 is equal to the cell mean of category 3 . contrast {race -1 1 0} {race -1 0 1}

--------------------------------------------------------------------------- Setup for two-way model . webuse bpchange . anova bpchange dose##gender

Simple effects of gender . contrast r.gender@dose

Reverse adjacent simple effects of dose . contrast ar.dose@gender

Interaction effects decomposed into individual contrasts . contrast ar.dose#r.gender

Main effects decomposed into individual contrasts . contrast ar.dose r.gender

Partial interaction effects . contrast ar.dose#gender . contrast dose#r.gender

--------------------------------------------------------------------------- Setup for nested model . webuse sat . anova score method / class|method /

Simple effects of class nested within method . contrast class|method

Main effects with nested error term and reweighting of empty cells . contrast method / class|method, emptycells(reweight)

--------------------------------------------------------------------------- Setup for unbalanced data . webuse cholesterol

ANOVA model with unbalanced data . anova chol race##agegrp

Reference category effects treating all factors as balanced . contrast r.race

Reference category effects, using observed marginal frequencies . contrast r.race, asobserved

Grand mean contrasts using observed cell frequencies . contrast gw.race

Weighted grand mean contrasts, using observed marginal frequencies . contrast gw.race, asobserved wald cieffects

--------------------------------------------------------------------------- Setup for continuous covariate . webuse census3 . anova brate region##c.medage

Reference category effects of region on the intercept . contrast r.region

Reference category effects of region on the slope of medage . contrast r.region#c.medage

--------------------------------------------------------------------------- Setup for nonlinear model . webuse hospital . logistic satisfied hospital##illness

ANOVA-style table of tests for main effects and interaction effects . contrast hospital##illness

--------------------------------------------------------------------------- Setup for multivariate response . webuse jaw . mvreg y1 y2 y3 = gender##fracture

Test the effects of gender, fracture, and their interaction in the first equation . contrast gender##fracture

Test these effects in equation y2 . contrast gender##fracture, equation(y2)

Test the same effects for each equation, suppressing blank space between terms . contrast gender##fracture, atequations vsquish

Test for a marginal effect on the means between dependent variables . contrast _eqns

Test whether the main effects of gender differ between the dependent variables . contrast gender#_eqns

---------------------------------------------------------------------------

Video example

Introduction to contrasts in Stata: One-way ANOVA

Stored results

contrast stores the following in r():

Scalars r(df_r) variance degrees of freedom r(k_terms) number of terms in termlist r(level) confidence level of confidence intervals

Macros r(cmd) contrast r(cmdline) command as typed r(est_cmd) e(cmd) from original estimation results r(est_cmdline) e(cmdline) from original estimation results r(title) title in output r(overall) overall or empty r(emptycells) empspec from emptycells() r(mcmethod) method from mcompare() r(mctitle) title for method from mcompare() r(mcadjustall) adjustall or empty r(margin_method) asbalanced or asobserved

Matrices r(b) contrast estimates r(V) variance-covariance matrix of the contrast estimates r(error) contrast estimability codes; 0 means estimable, 8 means not estimable r(L) matrix of contrasts applied to the model coefficients r(table) matrix containing the contrasts with their standard errors, test statistics, p-values, and confidence intervals r(F) vector of F statistics; r(df_r) present r(chi2) vector of chi-squared statistics; r(df_r) not present r(p) vector of p-values corresponding to r(F) or r(chi2) r(df) vector of degrees of freedom corresponding to r(p) r(df2) vector of denominator degrees of freedom corresponding to r(F)

contrast with the post option stores the following in e():

Scalars e(df_r) variance degrees of freedom e(k_terms) number of terms in termlist

Macros e(cmd) contrast e(cmdline) command as typed e(est_cmd) e(cmd) from original estimation results e(est_cmdline) e(cmdline) from original estimation results e(title) title in output e(overall) overall or empty e(emptycells) empspec from emptycells() e(margin_method) asbalanced or asobserved e(properties) b V

Matrices e(b) contrast estimates e(V) variance-covariance matrix of the contrast estimates e(error) contrast estimability codes; 0 means estimable, 8 means not estimable e(L) matrix of contrasts applied to the model coefficients e(F) vector of unadjusted F statistics; e(df_r) present e(chi2) vector of chi-squared statistics; e(df_r) not present e(p) vector of unadjusted p-values corresponding to e(F) or e(chi2) e(df) vector of degrees of freedom corresponding to e(p) e(df2) vector of denominator degrees of freedom corresponding to e(F)


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