library( "urbin" ) maxLikLoaded <- require( "maxLik" ) mfxLoaded <- require( "mfx" ) if( !require( "sampleSelection" ) ) { q( save = "no" ) } options( digits = 4 ) # load data set data( "Mroz87", package = "sampleSelection" ) # create dummy variable for kids Mroz87$kids <- as.numeric( Mroz87$kids5 > 0 | Mroz87$kids618 > 0 ) ### linear in age estLogitLin <- glm( lfp ~ kids + age + educ, family = binomial(link = "logit"), data = Mroz87 ) summary( estLogitLin ) # mean values of the explanatory variables xMeanLin <- c( 1, colMeans( Mroz87[ , c( "kids", "age", "educ" ) ] ) ) # semi-elasticity of age without standard errors urbinEla( coef( estLogitLin ), xMeanLin, xPos = 3, model = "logit" ) # semi-elasticity of age based on numerical derivation 100 * ( predict( estLogitLin, newdata = as.data.frame( t( xMeanLin * c( 1, 1, 1.005, 1 ) ) ), type = "response" ) - predict( estLogitLin, newdata = as.data.frame( t( xMeanLin * c( 1, 1, 0.995, 1 ) ) ), type = "response" ) ) # partial derivatives of the semi-elasticity wrt the coefficients urbinEla( coef( estLogitLin ), xMeanLin, 3, seSimplify = FALSE, model = "logit" )$derivCoef # numerically computed partial derivatives of the semi-elasticity wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinEla( x, ... )$semEla }, t0 = coef( estLogitLin ), allXVal = xMeanLin, xPos = 3, model = "logit" ) ) } # simplified partial derivatives of the semi-elasticity wrt the coefficients urbinEla( coef( estLogitLin ), xMeanLin, 3, model = "logit", seSimplify = TRUE )$derivCoef # semi-elasticity of age with standard errors (full covariance matrix) urbinEla( coef( estLogitLin ), xMeanLin, 3, model = "logit", vcov( estLogitLin ) ) # semi-elasticity of age with standard errors (only standard errors) urbinEla( coef( estLogitLin ), xMeanLin, 3, model = "logit", sqrt( diag( vcov( estLogitLin ) ) ), seSimplify = FALSE ) # semi-elasticity of age with standard errors (only standard errors, simplified) urbinEla( coef( estLogitLin ), xMeanLin, 3, model = "logit", sqrt( diag( vcov( estLogitLin ) ) ) ) # semi-elasticity of age based on partial derivative calculated by the mfx package if( mfxLoaded ) { estLogitLinMfx <- logitmfx( lfp ~ kids + age + educ, data = Mroz87 ) print( estLogitLinMfx$mfxest[ "age", 1:2 ] * xMeanLin[ "age" ] ) } if( mfxLoaded ) { print( urbinEla( estLogitLinMfx$mfxest[ "age", 1 ], xMeanLin["age"], 1, iPos = 0, model = "lpm", estLogitLinMfx$mfxest[ "age", 2 ] ) ) } if( mfxLoaded ) { print( urbinEla( estLogitLinMfx$mfxest[ , 1 ], xMeanLin[-1], 2, iPos = 0, model = "lpm", estLogitLinMfx$mfxest[ , 2 ] ) ) } ### quadratic in age estLogitQuad <- glm( lfp ~ kids + age + I(age^2) + educ, family = binomial(link = "logit"), data = Mroz87 ) summary( estLogitQuad ) # mean values of the explanatory variables xMeanQuad <- c( xMeanLin[ 1:3 ], xMeanLin[3]^2, xMeanLin[4] ) # semi-elasticity of age without standard errors urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit" ) # semi-elasticity of age based on numerical derivation 100 * ( predict( estLogitQuad, newdata = as.data.frame( t( xMeanQuad * c( 1, 1, 1.005, 1.005^2, 1 ) ) ), type = "response" ) - predict( estLogitQuad, newdata = as.data.frame( t( xMeanQuad * c( 1, 1, 0.995, 0.995^2, 1 ) ) ), type = "response" ) ) # partial derivatives of the semi-elasticity wrt the coefficients urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", seSimplify = FALSE )$derivCoef # numerically computed partial derivatives of the semi-elasticity wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinEla( x, ... )$semEla }, t0 = coef( estLogitQuad ), allXVal = xMeanQuad, xPos = c( 3, 4 ), model = "logit" ) ) } # simplified partial derivatives of the semi-elasticity wrt the coefficients urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", seSimplify = TRUE )$derivCoef # semi-elasticity of age with standard errors (full covariance matrix) urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", vcov( estLogitQuad ) ) # semi-elasticity of age with standard errors (only standard errors) urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", sqrt( diag( vcov( estLogitQuad ) ) ), seSimplify = FALSE ) # semi-elasticity of age with standard errors (only standard errors, simplified) urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", sqrt( diag( vcov( estLogitQuad ) ) ) ) # semi-elasticity of age with standard errors (only standard errors, xMeanSd) urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", sqrt( diag( vcov( estLogitQuad ) ) ), xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ), seSimplify = FALSE ) # semi-elasticity of age with standard errors (only standard errors, xMeanSd, simplified) urbinEla( coef( estLogitQuad ), xMeanQuad, c( 3, 4 ), model = "logit", sqrt( diag( vcov( estLogitQuad ) ) ), xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ) ) # semi-elasticity of age based on partial derivatives calculated by the mfx package # (differs from the above, because mean(age)^2 is not the same as mean(age^2)) if( mfxLoaded ) { estLogitQuadMfx <- logitmfx( lfp ~ kids + age + I(age^2) + educ, data = Mroz87 ) print( estLogitQuadMfx$mfxest[ "age", 1:2 ] * xMeanQuad[ "age" ] + 2 * estLogitQuadMfx$mfxest[ "I(age^2)", 1:2 ] * xMeanQuad[ "age" ]^2 ) } if( mfxLoaded ) { print( urbinEla( estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 1 ], xMeanQuad["age"], 1:2, iPos = 0, model = "lpm", estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 2 ] ) ) } if( mfxLoaded ) { print( urbinEla( estLogitQuadMfx$mfxest[ , 1 ], xMeanQuad[-1], 2:3, iPos = 0, model = "lpm", estLogitQuadMfx$mfxest[ , 2 ] ) ) } if( mfxLoaded ) { print( urbinEla( estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 1 ], xMeanQuad["age"], 1:2, iPos = 0, model = "lpm", estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 2 ], xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ) ) ) } if( mfxLoaded ) { print( urbinEla( estLogitQuadMfx$mfxest[ , 1 ], xMeanQuad[-1], 2:3, iPos = 0, model = "lpm", estLogitQuadMfx$mfxest[ , 2 ], xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ) ) ) } ### age is interval-coded (age is in the range 30-60) # create dummy variables for age intervals Mroz87$age30.37 <- Mroz87$age >= 30 & Mroz87$age <= 37 Mroz87$age38.44 <- Mroz87$age >= 38 & Mroz87$age <= 44 Mroz87$age45.52 <- Mroz87$age >= 45 & Mroz87$age <= 52 Mroz87$age53.60 <- Mroz87$age >= 53 & Mroz87$age <= 60 all.equal( Mroz87$age30.37 + Mroz87$age38.44 + Mroz87$age45.52 + Mroz87$age53.60, rep( 1, nrow( Mroz87 ) ) ) # estimation estLogitInt <- glm( lfp ~ kids + age30.37 + age38.44 + age53.60 + educ, family = binomial(link = "logit"), data = Mroz87 ) summary( estLogitInt ) # mean values of the explanatory variables xMeanInt <- c( xMeanLin[1:2], mean( Mroz87$age30.37 ), mean( Mroz87$age38.44 ), mean( Mroz87$age53.60 ), xMeanLin[4] ) # semi-elasticity of age without standard errors urbinElaInt( coef( estLogitInt ), xMeanInt, c( 3, 4, 0, 5 ), c( 30, 37.5, 44.5, 52.5, 60 ), model = "logit" ) # semi-elasticities based on numerical derivation Mroz87Lower <- Mroz87 Mroz87Lower$age <- Mroz87$age * 0.95 Mroz87Lower$age30.37 <- Mroz87Lower$age <= 37.5 Mroz87Lower$age38.44 <- Mroz87Lower$age > 37.5 & Mroz87Lower$age <= 44.5 Mroz87Lower$age45.52 <- Mroz87Lower$age > 44.5 & Mroz87Lower$age <= 52.5 Mroz87Lower$age53.60 <- Mroz87Lower$age > 52.5 all.equal( Mroz87Lower$age30.37 + Mroz87Lower$age38.44 + Mroz87Lower$age45.52 + Mroz87Lower$age53.60, rep( 1, nrow( Mroz87 ) ) ) Mroz87Upper <- Mroz87 Mroz87Upper$age <- Mroz87$age * 1.05 Mroz87Upper$age30.37 <- Mroz87Upper$age <= 37.5 Mroz87Upper$age38.44 <- Mroz87Upper$age > 37.5 & Mroz87Upper$age <= 44.5 Mroz87Upper$age45.52 <- Mroz87Upper$age > 44.5 & Mroz87Upper$age <= 52.5 Mroz87Upper$age53.60 <- Mroz87Upper$age > 52.5 all.equal( Mroz87Upper$age30.37 + Mroz87Upper$age38.44 + Mroz87Upper$age45.52 + Mroz87Upper$age53.60, rep( 1, nrow( Mroz87 ) ) ) 10 * mean( predict( estLogitInt, newdata = Mroz87Upper, type = "response" ) - predict( estLogitInt, newdata = Mroz87Lower, type = "response" ) ) Mroz87LowerMean <- Mroz87Lower Mroz87UpperMean <- Mroz87Upper Mroz87LowerMean$kids <- Mroz87UpperMean$kids <- xMeanInt[ "kids" ] Mroz87LowerMean$educ <- Mroz87UpperMean$educ <- xMeanInt[ "educ" ] 10 * mean( predict( estLogitInt, newdata = Mroz87UpperMean, type = "response" ) - predict( estLogitInt, newdata = Mroz87LowerMean, type = "response" ) ) # partial derivatives of the semi-elasticity wrt the coefficients urbinElaInt( coef( estLogitInt ), xMeanInt, c( 3, 4, 0, 5 ), c( 30, 37.5, 44.5, 52.5, 60 ), model = "logit" )$derivCoef # numerically computed partial derivatives of the semi-elasticity wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinElaInt( x, ... )$semEla }, t0 = coef( estLogitInt ), allXVal = xMeanInt, xPos = c( 3, 4, 0, 5 ), xBound = c( 30, 37.5, 44.5, 52.5, 60 ), model = "logit" ) ) } # semi-elasticity of age with standard errors (full covariance matrix) urbinElaInt( coef( estLogitInt ), xMeanInt, c( 3, 4, 0, 5 ), c( 30, 37.5, 44.5, 52.5, 60 ), model = "logit", allCoefVcov = vcov( estLogitInt ) ) # semi-elasticity of age with standard errors (only standard errors) urbinElaInt( coef( estLogitInt ), xMeanInt, c( 3, 4, 0, 5 ), c( 30, 37.5, 44.5, 52.5, 60 ), model = "logit", allCoefVcov = sqrt( diag( vcov( estLogitInt ) ) ) ) # semi-elasticity of age based on partial derivatives calculated by the mfx package if( mfxLoaded ) { estLogitIntMfx <- logitmfx( lfp ~ kids + age30.37 + age38.44 + age53.60 + educ, data = Mroz87 ) print( urbinElaInt( estLogitIntMfx$mfxest[ 2:4, 1 ], xMeanInt[ 3:5 ], c( 1, 2, 0, 3 ), iPos = 0, c( 30, 37.5, 44.5, 52.5, 60 ), model = "lpm", estLogitIntMfx$mfxest[ 2:4, 2 ] ) ) } if( mfxLoaded ) { print( urbinElaInt( estLogitIntMfx$mfxest[ , 1 ], xMeanInt[ -1 ], c( 2, 3, 0, 4 ), iPos = 0, c( 30, 37.5, 44.5, 52.5, 60 ), model = "lpm", estLogitIntMfx$mfxest[ , 2 ] ) ) } ### effect of age changing between discrete intervals ### if age is used as linear explanatory variable # mean values of the 'other' explanatory variables xMeanLinInt <- c( xMeanLin[ 1:2 ], NA, xMeanLin[4] ) # effects of age changing from the 30-40 interval to the 50-60 interval # without standard errors urbinEffInt( coef( estLogitLin ), allXVal = xMeanLinInt, xPos = 3, refBound = c( 30, 40 ), intBound = c( 50, 60 ), model = "logit" ) # effects of age changing from the 30-40 interval to the 50-60 interval # based on predicted values predict( estLogitLin, newdata = as.data.frame( t( replace( xMeanLin, 3, 55 ) ) ), type = "response" ) - predict( estLogitLin, newdata = as.data.frame( t( replace( xMeanLin, 3, 35 ) ) ), type = "response" ) # partial derivatives of the semi-elasticity wrt the coefficients urbinEffInt( coef( estLogitLin ), xMeanLinInt, 3, c( 30, 40 ), c( 50, 60 ), model = "logit" )$derivCoef # numerically computed partial derivatives of the semi-elasticity wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinEffInt( x, ... )$effect }, t0 = coef( estLogitLin ), allXVal = xMeanLinInt, xPos = 3, refBound = c( 30, 40 ), intBound = c( 50, 60 ), model = "logit" ) ) } # effects of age changing from the 30-40 interval to the 50-60 interval # (full covariance matrix) urbinEffInt( coef( estLogitLin ), xMeanLinInt, 3, c( 30, 40 ), c( 50, 60 ), model = "logit", allCoefVcov = vcov( estLogitLin ) ) # effects of age changing from the 30-40 interval to the 50-60 interval # (only standard errors) urbinEffInt( coef( estLogitLin ), allXVal = xMeanLinInt, xPos = 3, refBound = c( 30, 40 ), intBound = c( 50, 60 ), model = "logit", allCoefVcov = sqrt( diag( vcov( estLogitLin ) ) ) ) # semi-elasticity of age based on partial derivative calculated by the mfx package if( mfxLoaded ) { print( urbinEffInt( estLogitLinMfx$mfxest[ "age", 1 ], NULL, 1, iPos = 0, c( 30, 40 ), c( 50, 60 ), model = "lpm", estLogitLinMfx$mfxest[ "age", 2 ] ) ) } if( mfxLoaded ) { print( urbinEffInt( estLogitLinMfx$mfxest[ , 1 ], NULL, 2, iPos = 0, c( 30, 40 ), c( 50, 60 ), model = "lpm", estLogitLinMfx$mfxest[ , 2 ] ) ) } ### effect of age changing between discrete intervals ### if age is used as linear and quadratic explanatory variable # mean values of the 'other' explanatory variables xMeanQuadInt <- c( xMeanLin[ 1:2 ], NA, NA, xMeanLin[4] ) # effects of age changing from the 30-40 interval to the 50-60 interval # without standard errors urbinEffInt( coef( estLogitQuad ), allXVal = xMeanQuadInt, xPos = c( 3, 4 ), refBound = c( 30, 40 ), intBound = c( 50, 60 ), model = "logit" ) # effects of age changing from the 30-40 interval to the 50-60 interval # based on predicted values predict( estLogitQuad, newdata = as.data.frame( t( replace( xMeanQuad, 3:4, c( 55, 55^2 ) ) ) ), type = "response" ) - predict( estLogitQuad, newdata = as.data.frame( t( replace( xMeanQuad, 3:4, c( 35, 35^2 ) ) ) ), type = "response" ) # partial derivatives of the effect wrt the coefficients urbinEffInt( coef( estLogitQuad ), xMeanQuadInt, c( 3, 4 ), c( 30, 40 ), c( 50, 60 ), model = "logit" )$derivCoef # numerically computed partial derivatives of the effect wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinEffInt( x, ... )$effect }, t0 = coef( estLogitQuad ), allXVal = xMeanQuadInt, xPos = c( 3, 4 ), refBound = c( 30, 40 ), intBound = c( 50, 60 ), model = "logit" ) ) } # effects of age changing from the 30-40 interval to the 50-60 interval # (full covariance matrix) urbinEffInt( coef( estLogitQuad ), xMeanQuadInt, c( 3, 4 ), c( 30, 40 ), c( 50, 60 ), model = "logit", allCoefVcov = vcov( estLogitQuad ) ) # effects of age changing from the 30-40 interval to the 50-60 interval # (only standard errors) urbinEffInt( coef( estLogitQuad ), allXVal = xMeanQuadInt, xPos = c( 3, 4 ), refBound = c( 30, 40 ), intBound = c( 50, 60 ), model = "logit", allCoefVcov = sqrt( diag( vcov( estLogitQuad ) ) ) ) # effects of age changing from the 30-40 interval to the 50-60 interval # (standard errors + mean value and standard deviation of age) urbinEffInt( coef( estLogitQuad ), xMeanQuadInt, c( 3, 4 ), c( 30, 40 ), c( 50, 60 ), model = "logit", allCoefVcov = sqrt( diag( vcov( estLogitQuad ) ) ), xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ) ) # semi-elasticity of age based on partial derivative calculated by the mfx package if( mfxLoaded ) { print( urbinEffInt( estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 1 ], NULL, 1:2, iPos = 0, c( 30, 40 ), c( 50, 60 ), model = "lpm", estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 2 ] ) ) } if( mfxLoaded ) { print( urbinEffInt( estLogitQuadMfx$mfxest[ , 1 ], NULL, 2:3, iPos = 0, c( 30, 40 ), c( 50, 60 ), model = "lpm", estLogitQuadMfx$mfxest[ , 2 ] ) ) } if( mfxLoaded ) { print( urbinEffInt( estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 1 ], NULL, 1:2, iPos = 0, c( 30, 40 ), c( 50, 60 ), model = "lpm", estLogitQuadMfx$mfxest[ c( "age", "I(age^2)" ), 2 ], xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ) ) ) } if( mfxLoaded ) { print( urbinEffInt( estLogitQuadMfx$mfxest[ , 1 ], NULL, 2:3, iPos = 0, c( 30, 40 ), c( 50, 60 ), model = "lpm", estLogitQuadMfx$mfxest[ , 2 ], xMeanSd = c( mean( Mroz87$age ), sd( Mroz87$age ) ) ) ) } ### grouping and re-basing categorical variables ### effects of age changing from the 30-44 category to the 53-60 category # without standard errors urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( -1, -1, 1, 0 ), model = "logit" ) # effects calculated based on predicted values names( xMeanInt ) <- sub( "TRUE", "", names( coef( estLogitInt ) ) ) df30.37 <- df38.44 <- df45.52 <- df53.60 <- as.data.frame( t( xMeanInt ) ) df30.37[ , 3:5 ] <- c( TRUE, FALSE, FALSE ) df38.44[ , 3:5 ] <- c( FALSE, TRUE, FALSE ) df45.52[ , 3:5 ] <- c( FALSE, FALSE, FALSE ) df53.60[ , 3:5 ] <- c( FALSE, FALSE, TRUE ) predict( estLogitInt, newdata = df53.60, type = "response" ) - sum( Mroz87$age30.37 ) / sum( Mroz87$age30.37 + Mroz87$age38.44 ) * predict( estLogitInt, newdata = df30.37, type = "response" ) - sum( Mroz87$age38.44 ) / sum( Mroz87$age30.37 + Mroz87$age38.44 ) * predict( estLogitInt, newdata = df38.44, type = "response" ) # partial derivatives of the effect wrt the coefficients urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( -1, -1, 1, 0 ), model = "logit" )$derivCoef # numerically computed partial derivatives of the effect wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinEffCat( x, ... )$effect }, t0 = coef( estLogitInt ), allXVal = xMeanInt, xPos = c( 3:5 ), xGroups = c( -1, -1, 1, 0 ), model = "logit" ) ) } # with full covariance matrix urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( -1, -1, 1, 0 ), allCoefVcov = vcov( estLogitInt ), model = "logit" ) # with standard errors only urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( -1, -1, 1, 0 ), allCoefVcov = sqrt( diag( vcov( estLogitInt ) ) ), model = "logit" ) # semi-elasticity of age based on partial derivative calculated by the mfx package if( mfxLoaded ) { print( urbinEffCat( estLogitIntMfx$mfxest[ 2:4, 1 ], xMeanInt[ 3:5 ], c(1:3), c( -1, -1, 1, 0 ), iPos = 0, model = "lpm", estLogitIntMfx$mfxest[ 2:4, 2 ] ) ) } if( mfxLoaded ) { print( urbinEffCat( estLogitIntMfx$mfxest[ , 1 ], xMeanInt[ -1 ], c(2:4), c( -1, -1, 1, 0 ), iPos = 0, model = "lpm", estLogitIntMfx$mfxest[ , 2 ] ) ) } ### effects of age changing from the 53-60 category to the 38-52 category # without standard errors urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( 0, 1, -1, 1 ), model = "logit" ) # effects calculated based on predicted values sum( Mroz87$age38.44 ) / sum( Mroz87$age38.44 + Mroz87$age45.52 ) * predict( estLogitInt, newdata = df38.44, type = "response" ) + sum( Mroz87$age45.52 ) / sum( Mroz87$age38.44 + Mroz87$age45.52 ) * predict( estLogitInt, newdata = df45.52, type = "response" ) - predict( estLogitInt, newdata = df53.60, type = "response" ) # partial derivatives of the effect wrt the coefficients urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( 0, 1, -1, 1 ), model = "logit" )$derivCoef # numerically computed partial derivatives of the effect wrt the coefficients if( maxLikLoaded ) { print( numericGradient( function( x, ... ){ urbinEffCat( x, ... )$effect }, t0 = coef( estLogitInt ), allXVal = xMeanInt, xPos = c( 3:5 ), xGroups = c( 0, 1, -1, 1 ), model = "logit" ) ) } # with full covariance matrix urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( 0, 1, -1, 1 ), allCoefVcov = vcov( estLogitInt ), model = "logit" ) # with standard errors only urbinEffCat( coef( estLogitInt ), xMeanInt, c( 3:5 ), c( 0, 1, -1, 1 ), allCoefVcov = sqrt( diag( vcov( estLogitInt ) ) ), model = "logit" ) # semi-elasticity of age based on partial derivative calculated by the mfx package if( mfxLoaded ) { print( urbinEffCat( estLogitIntMfx$mfxest[ 2:4, 1 ], xMeanInt[ 3:5 ], c(1:3), c( 0, 1, -1, 1 ), iPos = 0, model = "lpm", estLogitIntMfx$mfxest[ 2:4, 2 ] ) ) } if( mfxLoaded ) { print( urbinEffCat( estLogitIntMfx$mfxest[ , 1 ], xMeanInt[ -1 ], c(2:4), c( 0, 1, -1, 1 ), iPos = 0, model = "lpm", estLogitIntMfx$mfxest[ , 2 ] ) ) }