### Missing data (SEM and regression via lavaan; listwise/fiml/multiple imputation)
### First, set the working directory where R will find the data
setwd("H:/data/User/Classes/multiv_13/YTs/YTSplit/Week 12 wmv - 2016/Wk12.R")
getwd()
## [1] "H:/data/User/Classes/multiv_13/YTs/YTSplit/Week 12 wmv - 2016/Wk12.R"
#########################################################################################
# Basic no-missing CFA
#########################################################################################
### First, set the working directory where R will find the data
setwd("H:/data/User/Classes/multiv_13/YTs/YTSplit/Week 12 wmv - 2016/Wk12.R")
getwd()
## [1] "H:/data/User/Classes/multiv_13/YTs/YTSplit/Week 12 wmv - 2016/Wk12.R"
### Read the data
a<- read.csv("class13_practice_2014_a.csv")
head(a)
## ï..const ID Executive Memory IQ PositiveAffect Extraversion WellBeing
## 1 1 1 51.50668 40.47171 49.26923 40.83332 49.94701 47.74377
## 2 1 2 54.58188 50.57909 57.74173 51.77439 43.00042 48.08132
## 3 1 3 56.10009 46.08254 48.32298 55.25798 46.25439 52.06285
## 4 1 4 51.61255 41.57124 53.78137 57.82760 53.41903 54.43308
## 5 1 5 54.44299 55.19846 56.92361 47.26358 52.73194 51.61065
## 6 1 6 55.10310 57.58064 54.32257 44.29526 46.84236 54.65610
## Hearing Vision Olfactory
## 1 55.32186 55.59998 52.90905
## 2 57.01612 49.93761 58.13047
## 3 49.56158 49.25982 49.82853
## 4 50.73262 52.23009 53.12584
## 5 37.57205 42.97714 41.98686
## 6 45.91365 45.88226 42.76423
library(lavaan)
## This is lavaan 0.6-7
## lavaan is BETA software! Please report any bugs.
a.mod<- ' cognitive =~ Executive + Memory + IQ
positivity =~ PositiveAffect + Extraversion + WellBeing
sensory =~ Hearing + Vision + Olfactory'
fit.a <- cfa(a.mod, data=a[3:11])
summary(fit.a, fit.measures=TRUE, standardized=TRUE)
fitmeasures(fit.a)
## lavaan 0.6-7 ended normally after 144 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 21
##
## Number of observations 240
##
## Model Test User Model:
##
## Test statistic 28.272
## Degrees of freedom 24
## P-value (Chi-square) 0.249
##
## Model Test Baseline Model:
##
## Test statistic 1146.066
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.996
## Tucker-Lewis Index (TLI) 0.994
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6671.657
## Loglikelihood unrestricted model (H1) -6657.521
##
## Akaike (AIC) 13385.314
## Bayesian (BIC) 13458.407
## Sample-size adjusted Bayesian (BIC) 13391.843
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.027
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.061
## P-value RMSEA <= 0.05 0.840
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cognitive =~
## Executive 1.000 8.659 0.878
## Memory 0.623 0.041 15.085 0.000 5.395 0.805
## IQ 0.634 0.038 16.808 0.000 5.488 0.890
## positivity =~
## PositiveAffect 1.000 6.539 0.823
## Extraversion 0.730 0.065 11.242 0.000 4.770 0.733
## WellBeing 0.695 0.057 12.143 0.000 4.544 0.826
## sensory =~
## Hearing 1.000 6.913 0.812
## Vision 0.714 0.055 12.931 0.000 4.935 0.774
## Olfactory 0.720 0.051 14.249 0.000 4.977 0.907
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cognitive ~~
## positivity 16.429 4.422 3.716 0.000 0.290 0.290
## sensory 4.715 4.337 1.087 0.277 0.079 0.079
## positivity ~~
## sensory 15.977 3.679 4.343 0.000 0.353 0.353
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Executive 22.292 3.573 6.239 0.000 22.292 0.229
## .Memory 15.800 1.845 8.564 0.000 15.800 0.352
## .IQ 7.864 1.380 5.698 0.000 7.864 0.207
## .PositiveAffect 20.397 3.212 6.349 0.000 20.397 0.323
## .Extraversion 19.613 2.298 8.533 0.000 19.613 0.463
## .WellBeing 9.590 1.537 6.240 0.000 9.590 0.317
## .Hearing 24.691 3.234 7.635 0.000 24.691 0.341
## .Vision 16.299 1.906 8.550 0.000 16.299 0.401
## .Olfactory 5.347 1.286 4.158 0.000 5.347 0.178
## cognitive 74.972 9.128 8.213 0.000 1.000 1.000
## positivity 42.757 6.052 7.065 0.000 1.000 1.000
## sensory 47.786 6.639 7.198 0.000 1.000 1.000
#########################################################################################
# CFA with listwise deletion and with FIML
#########################################################################################
# Listwise deletion (this code automatically invokes listwise by the program)
fit.b <- cfa(a.mod, data=b[3:11])
summary(fit.b, fit.measures=TRUE, standardized=TRUE)
fitmeasures(fit.b)
## lavaan 0.6-7 ended normally after 135 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 21
##
## Used Total
## Number of observations 229 240
##
## Model Test User Model:
##
## Test statistic 15.721
## Degrees of freedom 24
## P-value (Chi-square) 0.898
##
## Model Test Baseline Model:
##
## Test statistic 1114.744
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.012
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6329.768
## Loglikelihood unrestricted model (H1) -6321.908
##
## Akaike (AIC) 12701.536
## Bayesian (BIC) 12773.645
## Sample-size adjusted Bayesian (BIC) 12707.088
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.024
## P-value RMSEA <= 0.05 0.996
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cognitive =~
## Executive 1.000 8.517 0.831
## Memory 0.712 0.047 15.239 0.000 6.065 0.849
## IQ 0.667 0.041 16.217 0.000 5.680 0.919
## positivity =~
## PositiveAffect 1.000 6.258 0.815
## Extraversion 0.751 0.061 12.266 0.000 4.698 0.762
## WellBeing 0.779 0.058 13.431 0.000 4.872 0.898
## sensory =~
## Hearing 1.000 6.838 0.822
## Vision 0.688 0.057 12.098 0.000 4.706 0.759
## Olfactory 0.680 0.052 13.132 0.000 4.650 0.881
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cognitive ~~
## positivity 8.775 4.013 2.187 0.029 0.165 0.165
## sensory -1.268 4.316 -0.294 0.769 -0.022 -0.022
## positivity ~~
## sensory 5.430 3.263 1.664 0.096 0.127 0.127
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Executive 32.390 4.074 7.951 0.000 32.390 0.309
## .Memory 14.259 1.919 7.429 0.000 14.259 0.279
## .IQ 5.909 1.329 4.444 0.000 5.909 0.155
## .PositiveAffect 19.841 2.786 7.121 0.000 19.841 0.336
## .Extraversion 15.965 1.901 8.400 0.000 15.965 0.420
## .WellBeing 5.698 1.365 4.175 0.000 5.698 0.194
## .Hearing 22.466 3.327 6.752 0.000 22.466 0.325
## .Vision 16.266 1.952 8.333 0.000 16.266 0.424
## .Olfactory 6.252 1.328 4.708 0.000 6.252 0.224
## cognitive 72.544 9.718 7.465 0.000 1.000 1.000
## positivity 39.161 5.594 7.001 0.000 1.000 1.000
## sensory 46.763 6.642 7.041 0.000 1.000 1.000
anova(fit.b)
## Chi-Squared Test Statistic (unscaled)
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## Saturated 0 0.000
## Model 24 12702 12774 15.721 15.721 24 0.8979
library(lavaanPlot)
## Warning: package 'lavaanPlot' was built under R version 4.0.3
lavaanPlot(model = fit.b, sig=.05,stars=c("regress","latent","covs"),
node_options = list(shape = "box", fontname = "Arial"),
edge_options = list(color = "black"),
coefs = TRUE, covs = TRUE, stand=TRUE)
#FIML -- note that this will drop the one case -- as in Little's test above -- that contains
#completely missing values.
fit.c <- cfa(a.mod, data=b[3:11], missing="FIML", meanstructure=TRUE)
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 157
summary(fit.c, fit.measures=TRUE, standardized=TRUE)
fitmeasures(fit.c)
## lavaan 0.6-7 ended normally after 168 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 30
##
## Used Total
## Number of observations 239 240
## Number of missing patterns 10
##
## Model Test User Model:
##
## Test statistic 15.584
## Degrees of freedom 24
## P-value (Chi-square) 0.902
##
## Model Test Baseline Model:
##
## Test statistic 1147.315
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.011
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6527.437
## Loglikelihood unrestricted model (H1) -6519.645
##
## Akaike (AIC) 13114.873
## Bayesian (BIC) 13219.167
## Sample-size adjusted Bayesian (BIC) 13124.076
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.023
## P-value RMSEA <= 0.05 0.997
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.028
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cognitive =~
## Executive 1.000 8.666 0.837
## Memory 0.692 0.045 15.518 0.000 5.994 0.843
## IQ 0.659 0.040 16.630 0.000 5.714 0.921
## positivity =~
## PositiveAffect 1.000 6.243 0.816
## Extraversion 0.749 0.061 12.367 0.000 4.679 0.762
## WellBeing 0.780 0.057 13.655 0.000 4.869 0.899
## sensory =~
## Hearing 1.000 6.874 0.824
## Vision 0.679 0.056 12.140 0.000 4.665 0.752
## Olfactory 0.690 0.051 13.473 0.000 4.740 0.888
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cognitive ~~
## positivity 8.090 4.009 2.018 0.044 0.150 0.150
## sensory -0.543 4.328 -0.126 0.900 -0.009 -0.009
## positivity ~~
## sensory 6.203 3.254 1.907 0.057 0.145 0.145
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Executive 50.967 0.671 75.989 0.000 50.967 4.923
## .Memory 50.293 0.462 108.909 0.000 50.293 7.073
## .IQ 50.500 0.402 125.510 0.000 50.500 8.139
## .PositiveAffect 50.661 0.497 101.857 0.000 50.661 6.621
## .Extraversion 50.098 0.399 125.527 0.000 50.098 8.156
## .WellBeing 50.229 0.352 142.737 0.000 50.229 9.276
## .Hearing 49.887 0.542 92.126 0.000 49.887 5.976
## .Vision 50.362 0.402 125.273 0.000 50.362 8.123
## .Olfactory 50.097 0.346 144.836 0.000 50.097 9.386
## cognitive 0.000 0.000 0.000
## positivity 0.000 0.000 0.000
## sensory 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Executive 32.055 4.069 7.878 0.000 32.055 0.299
## .Memory 14.630 1.895 7.720 0.000 14.630 0.289
## .IQ 5.839 1.326 4.403 0.000 5.839 0.152
## .PositiveAffect 19.569 2.723 7.186 0.000 19.569 0.334
## .Extraversion 15.835 1.846 8.578 0.000 15.835 0.420
## .WellBeing 5.615 1.332 4.215 0.000 5.615 0.191
## .Hearing 22.428 3.278 6.841 0.000 22.428 0.322
## .Vision 16.679 1.935 8.620 0.000 16.679 0.434
## .Olfactory 6.020 1.331 4.523 0.000 6.020 0.211
## cognitive 75.103 9.768 7.689 0.000 1.000 1.000
## positivity 38.981 5.488 7.103 0.000 1.000 1.000
## sensory 47.258 6.613 7.147 0.000 1.000 1.000
anova(fit.c)
## Chi-Squared Test Statistic (unscaled)
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## Saturated 0 0.000
## Model 24 13115 13219 15.584 15.584 24 0.9025
# multiple imputation with ten imputations
# Warning, you get a "solution has not been found" warning, but the values seem fine.
# Can't seem to find if this is meaningful or not, or how to fix it
# In general, MI is not needed when you can do FIML, anyway. The df seem fishy for some of
# these values
library(semTools)
## Warning: package 'semTools' was built under R version 4.0.3
##
## ###############################################################################
## This is semTools 0.5-3
## All users of R (or SEM) are invited to submit functions or ideas for functions.
## ###############################################################################
fit.d <- runMI(a.mod, data=b[3:11], m = 10, miPackage="Amelia", seed=12345, meanstructure=TRUE,
fun="cfa")
## Loading required namespace: Amelia
## ##
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.6, built: 2019-11-24)
## ## Copyright (C) 2005-2020 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##
summary(fit.d)
#fitmeasures(fit.d)
## lavaan.mi object based on 10 imputed data sets.
## See class?lavaan.mi help page for available methods.
##
## Convergence information:
## The model converged on 10 imputed data sets
##
## Rubin's (1987) rules were used to pool point and SE estimates across 10 imputed data sets, and to calculate degrees of freedom for each parameter's t test and CI.
##
## Parameter Estimates:
## Warning in if (attr(x, "information") == "observed") {: the condition has length
## > 1 and only the first element will be used
## Warning in cbind(c1, c2, deparse.level = 0): number of rows of result is not a
## multiple of vector length (arg 1)
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Expected
## Standard errors Structured
## Information Structured
##
## Latent Variables:
## Estimate Std.Err t-value df P(>|t|)
## cognitive =~
## Executive 1.000
## Memory 0.693 0.045 15.464 Inf 0.000
## IQ 0.660 0.040 16.590 Inf 0.000
## positivity =~
## PositiveAffect 1.000
## Extraversion 0.749 0.060 12.492 Inf 0.000
## WellBeing 0.777 0.057 13.711 7140.782 0.000
## sensory =~
## Hearing 1.000
## Vision 0.682 0.056 12.196 7453.255 0.000
## Olfactory 0.692 0.052 13.360 Inf 0.000
##
## Covariances:
## Estimate Std.Err t-value df P(>|t|)
## cognitive ~~
## positivity 8.041 4.020 2.000 Inf 0.045
## sensory -0.507 4.340 -0.117 Inf 0.907
## positivity ~~
## sensory 6.338 3.244 1.953 Inf 0.051
##
## Intercepts:
## Estimate Std.Err t-value df P(>|t|)
## .Executive 50.956 0.677 75.267 Inf 0.000
## .Memory 50.287 0.465 108.258 Inf 0.000
## .IQ 50.499 0.406 124.465 Inf 0.000
## .PositiveAffect 50.681 0.501 101.234 Inf 0.000
## .Extraversion 50.109 0.402 124.666 Inf 0.000
## .WellBeing 50.235 0.354 141.853 Inf 0.000
## .Hearing 49.882 0.545 91.572 Inf 0.000
## .Vision 50.366 0.405 124.304 Inf 0.000
## .Olfactory 50.093 0.349 143.478 Inf 0.000
## cognitive 0.000
## positivity 0.000
## sensory 0.000
##
## Variances:
## Estimate Std.Err t-value df P(>|t|)
## .Executive 32.238 4.070 7.920 5748.949 0.000
## .Memory 14.465 1.887 7.667 Inf 0.000
## .IQ 5.863 1.321 4.438 5521.073 0.000
## .PositiveAffect 19.438 2.715 7.159 Inf 0.000
## .Extraversion 15.805 1.857 8.509 Inf 0.000
## .WellBeing 5.658 1.333 4.244 2519.701 0.000
## .Hearing 22.517 3.293 6.839 Inf 0.000
## .Vision 16.607 1.942 8.551 Inf 0.000
## .Olfactory 6.073 1.342 4.524 9047.015 0.000
## cognitive 75.081 9.858 7.616 Inf 0.000
## positivity 39.249 5.508 7.126 8388.965 0.000
## sensory 46.965 6.589 7.127 Inf 0.000
fitMeasures(fit.d, "chisq")
## chisq
## 15.585
anova(fit.d)
## F df1 df2 pvalue
## 0.649 24.000 299069.254 0.902
## ariv fmi npar ntotal
## 0.027 0.026 30.000 239.000
## logl unrestricted.logl aic bic
## -6606.662 -6598.658 13273.324 13377.618
## bic2
## 13282.526
#########################################################################################
# Easy linear regression with listwise deletion, and with FIML and MI
#########################################################################################
library("survey")
## Loading required package: grid
## Loading required package: Matrix
## Loading required package: survival
##
## Attaching package: 'survey'
## The following object is masked from 'package:graphics':
##
## dotchart
library("mice")
##
## Attaching package: 'mice'
## The following objects are masked from 'package:base':
##
## cbind, rbind
#install.packages("mitools")
library("mitools")
library("semTools")
library("lavaan")
#install.packages("lavaan.survey")
library("lavaan.survey")
## Warning: package 'lavaan.survey' was built under R version 4.0.3
#regression
#set up the basic model
b_examp <- ' ## regressions
Positive Affect ~ Executive + Hearing
'
#Listwise deletion
b_examp0<-sem(b_examp, data = b, meanstructure = TRUE, fixed.x=FALSE)
summary(b_examp0)
## lavaan 0.6-7 ended normally after 18 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 9
##
## Used Total
## Number of observations 233 240
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## PositiveAffect ~
## Executive 0.138 0.048 2.879 0.004
## Hearing 0.124 0.059 2.106 0.035
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Executive ~~
## Hearing -3.907 5.551 -0.704 0.482
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .PositiveAffect 37.487 3.929 9.542 0.000
## Executive 50.957 0.669 76.185 0.000
## Hearing 49.761 0.543 91.616 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PositiveAffect 55.470 5.139 10.794 0.000
## Executive 104.236 9.657 10.794 0.000
## Hearing 68.736 6.368 10.794 0.000
#FIML - again, two cases where all three variables are missing will be dropped
b_examp1<-sem(b_examp, data = b, missing="FIML", meanstructure = TRUE, fixed.x=FALSE)
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 80 157
summary(b_examp1)
#fitmeasures(b_exampl)
## lavaan 0.6-7 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 9
##
## Used Total
## Number of observations 238 240
## Number of missing patterns 5
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## PositiveAffect ~
## Executive 0.139 0.048 2.922 0.003
## Hearing 0.124 0.059 2.103 0.035
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## Executive ~~
## Hearing -3.657 5.595 -0.654 0.513
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .PositiveAffect 37.348 3.923 9.521 0.000
## Executive 50.976 0.674 75.634 0.000
## Hearing 49.846 0.540 92.308 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .PositiveAffect 55.427 5.114 10.838 0.000
## Executive 107.673 9.891 10.886 0.000
## Hearing 68.818 6.335 10.863 0.000
#Multiple imputation
#install.packages("Amelia")
library(Amelia)
# multiple imputation with five imputations; this one is going to have a problem with some of
# the other variables in the data frame, so I limited this to "b_subset" data frame, which
# includes only the variables we care about, from above
b_examp2 <- runMI(b_examp, data=b_subset, m = 10, miPackage="Amelia", seed=12345,
fun="sem", fixed.x=FALSE)
summary(b_examp2)
#fitmeasures(b_examp2)
## lavaan.mi object based on 10 imputed data sets.
## See class?lavaan.mi help page for available methods.
##
## Convergence information:
## The model converged on 10 imputed data sets
##
## Rubin's (1987) rules were used to pool point and SE estimates across 10 imputed data sets, and to calculate degrees of freedom for each parameter's t test and CI.
##
## Parameter Estimates:
## Warning in if (attr(x, "information") == "observed") {: the condition has length
## > 1 and only the first element will be used
## Warning in if (attr(x, "information") == "observed") {: number of rows of result
## is not a multiple of vector length (arg 1)
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Expected
## Standard errors Structured
## Information Structured
##
## Regressions:
## Estimate Std.Err t-value df P(>|t|)
## PositiveAffect ~
## Executive 0.130 0.047 2.754 7374.213 0.006
## Hearing 0.137 0.059 2.332 Inf 0.020
##
## Covariances:
## Estimate Std.Err t-value df P(>|t|)
## Executive ~~
## Hearing -3.558 5.648 -0.630 Inf 0.529
##
## Variances:
## Estimate Std.Err t-value df P(>|t|)
## .PositiveAffect 55.696 5.148 10.820 Inf 0.000
## Executive 107.319 9.918 10.820 Inf 0.000
## Hearing 69.482 6.422 10.819 Inf 0.000