R/assign.pctiles.R
In ejanalysis/ejanalysis: Tools for Environmental Justice (EJ) Analysis
Defines functions
assign.pctiles
Documented in
assign.pctiles
#' @title Assign percentiles to vector of values (weighted, by zone)
#'
#' @description For the vector, look at the distribution of values across all rows in a given zone (e.g., places in zone),
#' and find what percentile a given value is at.
#' @details Relies on the [Hmisc::wtd.Ecdf()] function.
#' COULD BE RECODED TO BE FASTER USING data.table package *** see notes in [rollup.pct()] and [rollup()]
#' Could also add parameter like in rank(), na.last,
#' defining na.rm but also where to rank NA values if included, etc.
#'
#' Default now is like na.last=NA, but like na.last='last' if na.rm=FALSE
#'
#' ****Could also add parameter like in rank(), ties.method, defining if ties get min, max, or mean of percentiles initially assigned to ties.
#' Default for ties up to mid2022 was like ties.method=max ?
#' But EJScreen will redefine percentiles to set tied values at lower end of that group, min
#'
#' @param values vector, required, with numeric values. To do this with a matrix, see [make.pctile.cols()]
#' @param weights Optional, NULL by default (not fully tested), vector of weights for weighted percentiles (e.g., population weighted).
#' @param na.rm NOT IMPLEMENTED HERE. Logical, optional, TRUE by default. Should NA values (missing data) be removed first to get percentile of those with valid data.
#' If FALSE, NA values are treated as being at the high percentiles.
#' @param zone Optional, NULL by default, defines subsets of rows, so a percentile is found among rows that are within a given zone only.
#' @return Returns a numeric vector same size as x, but if zone is specified, provides percentile with given zone.
#' @seealso
#' [make.bin.pctile.cols()] to call functions below, converting columns of values to percentiles and then bins
#' [assign.pctiles()] for one vector, assign (weighted) percentile (quantile) to each value within its zone (subset)
#' [assign.pctiles.alt2()] as an alternative method, to replicate assign.pctiles, but not by zone
#' [get.pctile()] to get (weighted) percentile of just 1+ values within given vector of values
#' [make.pctile.cols()] for a data.frame, assign percentiles, return a same-sized df that is wtd.quantile of each value within its column
#' [make.pctile.cols.alt2()] as an alternative method, to replicate make.pctile.cols
#' [assign.map.bins()] for one vector (or data.frame) of values (e.g. percentiles), return same-sized df that is bin number (map color bin) using preset breaks.
#' [make.bin.cols()] for a data.frame of values (e.g. percentiles), return same-sized df that is bin number (map color bin) using preset breaks.
#' [write.pctiles()] to save file that is lookup table of percentiles for columns of a data.frame
#' [write.pctiles.by.zone()] to save file that is lookup table of percentiles for columns of a data.frame, for each geographic zone (subset of rows)
#' [write.wtd.pctiles()] to save file that is lookup table of weighted percentiles for columns of a data.frame
#' [write.wtd.pctiles.by.zone()] to save file that is lookup table of weighted percentiles for columns of a data.frame, for each geographic zone (subset of rows)
#' [lookup.pctile()] to look up current approx weighted percentiles in a lookup table that is already in global memory
#'
#' @examples
#' x <- c(30, 40, 50, 12,12,5,5,13,13,13,13,13,8,9,9,9,9,9,10:20,20,20,20,21:30)
#' wts <- rep(c(2,3), length(x)/2)
#' cbind(wts, x, PCTILE=assign.pctiles(x,wts))
#'
#' # PERCENTILE OF ALL, NOT JUST THOSE WITH VALID DATA, IF na.rm=FALSE,
#' # but then NA values preclude high percentiles:
#' x <- c(NA, NA, NA, NA,NA,NA,NA,NA,NA,NA,13,13,8,9,9,9,9,9,10:20,20,20,20,21:30)
#' wts <- rep(c(2,3), length(x)/2)
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=FALSE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=TRUE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#'
#' V=9
#' sum(wts[!is.na(x) & x <= V]) / sum(wts[!is.na(x)])
#'
#' #A value (V) being at this PCTILE% means that (assuming na.rm=TRUE):
#'
#' # V >= x for PCTILE% of wts (for non-NA x), so
#' # V < x for 100% - PCTILE% of wts (for non-NA x), or
#' # PCTILE% of all wts have V >= x (for non-NA x), so
#' # 100% - PCTILE% of all wts have V < x (for non-NA x).
#'
#' x <- c(32, NA, NA, NA,NA,NA,NA,NA,NA,NA,13,13,8,9,9,9,9,9,10:20,20,NA,20,21:30)
#' wts <- rep(c(2,3), length(x)/2)
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=FALSE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=TRUE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#'
#' \dontrun{
#' What is environmental score at given percentile?
#' ejanalysis::lookup.pctile(40,'cancer',lookupUSA)
#' # [1] 84
#' ejanalysis::lookup.pctile(40,'cancer',lookupStates,'WV')
#' # [1] 93
#' # What is percentile of given environmental score?
#' ejscreen::lookupUSA[lookupUSA$PCTILE=='84' ,'cancer']
#' # [1] 39.83055
#' ejscreen::lookupStates[lookupStates$PCTILE=='84' & lookupStates$REGION =='WV','cancer']
#' # [1] 33.36371
#' }
#'
#' @export
#'
assign.pctiles <- function(values, weights=NULL, zone=NULL, na.rm=TRUE) {
if (all(weights == 1)) {weights <- NULL} # to work with make.pctile.cols( where default was weights=1 )
# FUNCTION TO ASSIGN THE EXACT WEIGHTED (or unweighted) PERCENTILE NUMBER TO EACH LOCATION'S RAW INDICATOR SCORE
if (!missing(na.rm)) {warning('na.rm is not implemented yet')}
#require(Hmisc)
if (is.null(zone)) {
wtd.Ecdf.results <- Hmisc::wtd.Ecdf(values, weights=weights, normwt = FALSE, type='i/n', na.rm=TRUE)
# If the first CDF estimate is greater than zero, a point (min(x),0) is placed at the beginning of the estimates.
if (length(wtd.Ecdf.results$x) == 1+ length(unique(values)) ) { wtd.Ecdf.results$x <- wtd.Ecdf.results$x[-1]; wtd.Ecdf.results$ecdf <- wtd.Ecdf.results$ecdf[-1] }
# This finds the rank of each value # but note this is to index by number, not character value which would find the first of a given value via [as.character( $x)]
myindex <- findInterval(values, wtd.Ecdf.results$x)
myindex[myindex==0] <- 1 # if for some reason the minimum value doesn't match, which has occurred in testing
exact.wtd.pctile <- wtd.Ecdf.results$ecdf[ myindex ]
} else {
# **** this calculation by zone could be redone using aggregate, summarize, data.table functions etc. instead of a for loop:
exact.wtd.pctile <- vector(length=length(values))
for (z in unique(zone)) {
myvals <- values[zone==z]
mywts <- weights[zone==z]
if (all(is.na(myvals)) | all(is.na(mywts))) {
# add code here for when zone has no valid weights or no valid values due to missing values
exact.wtd.pctile[zone==z] <- NA
} else {
wtd.Ecdf.results <- Hmisc::wtd.Ecdf(myvals, weights=mywts, normwt = FALSE, type='i/n', na.rm=TRUE)
# If the first CDF estimate is greater than zero, a point (min(x),0) is placed at the beginning of the estimates.
if (length(wtd.Ecdf.results$x) == 1+ length(unique(myvals)) ) { wtd.Ecdf.results$x <- wtd.Ecdf.results$x[-1]; wtd.Ecdf.results$ecdf <- wtd.Ecdf.results$ecdf[-1] }
# This finds the rank of each value
myindex <- findInterval(myvals, wtd.Ecdf.results$x)
myindex[myindex==0] <- 1 # if for some reason the minimum value doesn't match, which has occurred in testing
exact.wtd.pctile[zone==z] <- wtd.Ecdf.results$ecdf[ myindex ]
}
}
}
return(exact.wtd.pctile)
############################################################## #
# NOTES ON THIS FUNCTION
# For documentation of wtd.Ecdf() from Hmisc package, see
# http://127.0.0.1:26624/library/Hmisc/html/wtd.stats.html
# wtd.Ecdf returns a list whose elements x and Ecdf correspond to unique sorted values of x.
#
# Min and max percentiles assigned:
# Note that if the first CDF estimate is greater than zero, a point (min(x),0) is placed at the beginning of the estimates. [so we remove that since it is just confusing]
# There will never be exactly 0 assigned as the percentile.
# The smallest that may be assigned is 1/n and this is assigned to the min input if it is unique.
# If min is not unique, all those N ties for min of n total values are assigned N/n (not 1/n) as their percentile.
# There highest percentile assigned is exactly 1.00 -- This happens to the maximum value, and for any tied for the maximum.
#
# TIES: Ties in input values are all assigned the same percentile, the percentile at the upper end of that bin's range
# so if for example the top 3 values of 100 values are tied, they are all assigned 1.000 as the percentile & the next is assigned 0.97, etc.
#
# type="i/n" to use the inverse of the empirical distribution function, using, ... wt/T,
# where wt is the cumulative weight and T is the total weight (usually total sample size).
#
# For documentation on findInterval() function:
# http://127.0.0.1:26624/library/base/html/findInterval.html
#
# By the way, for unweighted quantiles, the following would do almost the same thing as using wtd.Ecdf(x, weights=NULL) but not exactly identical:
# exact.quantile <- function(x) { Fn<-ecdf(x); Fn(x) }
#
# **** Note that this assign.pctiles() function, which relies on wtd.Ecdf(),
# will ignore NA values, and return NA as the percentile assigned to those,
# and the other percentiles assigned are among valid (non-NA) values only.
# If na.rm=TRUE (default), this version treats NA values in input by excluding them from ranking,
# making their percentile NA and finding %iles among all valid values,
# so if there were 105 values with 5 being NA and the other 100 being unique numbers,
# this function would return 1-100 as the valid %iles and return "NA" as %ile for other 5.
# For example:
# 100 * assign.pctiles(c(1001:1100, rep(NA, 39)), na.rm=FALSE)
#
# returns the following:
#
#1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
#1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046
# 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
#1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069
# 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
#1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092
# 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92
#1093 1094 1095 1096 1097 1098 1099 1100 <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA>
# 93 94 95 96 97 98 99 100 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
#<NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA>
# NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
#<NA>
# NA
#
}
ejanalysis/ejanalysis documentation built on April 2, 2024, 10:12 a.m.
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Defines functions assign.pctiles
Documented in assign.pctiles
#' @title Assign percentiles to vector of values (weighted, by zone)
#'
#' @description For the vector, look at the distribution of values across all rows in a given zone (e.g., places in zone),
#' and find what percentile a given value is at.
#' @details Relies on the [Hmisc::wtd.Ecdf()] function.
#' COULD BE RECODED TO BE FASTER USING data.table package *** see notes in [rollup.pct()] and [rollup()]
#' Could also add parameter like in rank(), na.last,
#' defining na.rm but also where to rank NA values if included, etc.
#'
#' Default now is like na.last=NA, but like na.last='last' if na.rm=FALSE
#'
#' ****Could also add parameter like in rank(), ties.method, defining if ties get min, max, or mean of percentiles initially assigned to ties.
#' Default for ties up to mid2022 was like ties.method=max ?
#' But EJScreen will redefine percentiles to set tied values at lower end of that group, min
#'
#' @param values vector, required, with numeric values. To do this with a matrix, see [make.pctile.cols()]
#' @param weights Optional, NULL by default (not fully tested), vector of weights for weighted percentiles (e.g., population weighted).
#' @param na.rm NOT IMPLEMENTED HERE. Logical, optional, TRUE by default. Should NA values (missing data) be removed first to get percentile of those with valid data.
#' If FALSE, NA values are treated as being at the high percentiles.
#' @param zone Optional, NULL by default, defines subsets of rows, so a percentile is found among rows that are within a given zone only.
#' @return Returns a numeric vector same size as x, but if zone is specified, provides percentile with given zone.
#' @seealso
#' [make.bin.pctile.cols()] to call functions below, converting columns of values to percentiles and then bins
#' [assign.pctiles()] for one vector, assign (weighted) percentile (quantile) to each value within its zone (subset)
#' [assign.pctiles.alt2()] as an alternative method, to replicate assign.pctiles, but not by zone
#' [get.pctile()] to get (weighted) percentile of just 1+ values within given vector of values
#' [make.pctile.cols()] for a data.frame, assign percentiles, return a same-sized df that is wtd.quantile of each value within its column
#' [make.pctile.cols.alt2()] as an alternative method, to replicate make.pctile.cols
#' [assign.map.bins()] for one vector (or data.frame) of values (e.g. percentiles), return same-sized df that is bin number (map color bin) using preset breaks.
#' [make.bin.cols()] for a data.frame of values (e.g. percentiles), return same-sized df that is bin number (map color bin) using preset breaks.
#' [write.pctiles()] to save file that is lookup table of percentiles for columns of a data.frame
#' [write.pctiles.by.zone()] to save file that is lookup table of percentiles for columns of a data.frame, for each geographic zone (subset of rows)
#' [write.wtd.pctiles()] to save file that is lookup table of weighted percentiles for columns of a data.frame
#' [write.wtd.pctiles.by.zone()] to save file that is lookup table of weighted percentiles for columns of a data.frame, for each geographic zone (subset of rows)
#' [lookup.pctile()] to look up current approx weighted percentiles in a lookup table that is already in global memory
#'
#' @examples
#' x <- c(30, 40, 50, 12,12,5,5,13,13,13,13,13,8,9,9,9,9,9,10:20,20,20,20,21:30)
#' wts <- rep(c(2,3), length(x)/2)
#' cbind(wts, x, PCTILE=assign.pctiles(x,wts))
#'
#' # PERCENTILE OF ALL, NOT JUST THOSE WITH VALID DATA, IF na.rm=FALSE,
#' # but then NA values preclude high percentiles:
#' x <- c(NA, NA, NA, NA,NA,NA,NA,NA,NA,NA,13,13,8,9,9,9,9,9,10:20,20,20,20,21:30)
#' wts <- rep(c(2,3), length(x)/2)
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=FALSE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=TRUE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#'
#' V=9
#' sum(wts[!is.na(x) & x <= V]) / sum(wts[!is.na(x)])
#'
#' #A value (V) being at this PCTILE% means that (assuming na.rm=TRUE):
#'
#' # V >= x for PCTILE% of wts (for non-NA x), so
#' # V < x for 100% - PCTILE% of wts (for non-NA x), or
#' # PCTILE% of all wts have V >= x (for non-NA x), so
#' # 100% - PCTILE% of all wts have V < x (for non-NA x).
#'
#' x <- c(32, NA, NA, NA,NA,NA,NA,NA,NA,NA,13,13,8,9,9,9,9,9,10:20,20,NA,20,21:30)
#' wts <- rep(c(2,3), length(x)/2)
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=FALSE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#' cbind(wts, x, PCTILE.alt2=assign.pctiles.alt2(x, wts, na.rm=TRUE),
#' pctile=assign.pctiles(x,wts))[order(x),]
#'
#' \dontrun{
#' What is environmental score at given percentile?
#' ejanalysis::lookup.pctile(40,'cancer',lookupUSA)
#' # [1] 84
#' ejanalysis::lookup.pctile(40,'cancer',lookupStates,'WV')
#' # [1] 93
#' # What is percentile of given environmental score?
#' ejscreen::lookupUSA[lookupUSA$PCTILE=='84' ,'cancer']
#' # [1] 39.83055
#' ejscreen::lookupStates[lookupStates$PCTILE=='84' & lookupStates$REGION =='WV','cancer']
#' # [1] 33.36371
#' }
#'
#' @export
#'
assign.pctiles <- function(values, weights=NULL, zone=NULL, na.rm=TRUE) {
if (all(weights == 1)) {weights <- NULL} # to work with make.pctile.cols( where default was weights=1 )
# FUNCTION TO ASSIGN THE EXACT WEIGHTED (or unweighted) PERCENTILE NUMBER TO EACH LOCATION'S RAW INDICATOR SCORE
if (!missing(na.rm)) {warning('na.rm is not implemented yet')}
#require(Hmisc)
if (is.null(zone)) {
wtd.Ecdf.results <- Hmisc::wtd.Ecdf(values, weights=weights, normwt = FALSE, type='i/n', na.rm=TRUE)
# If the first CDF estimate is greater than zero, a point (min(x),0) is placed at the beginning of the estimates.
if (length(wtd.Ecdf.results$x) == 1+ length(unique(values)) ) { wtd.Ecdf.results$x <- wtd.Ecdf.results$x[-1]; wtd.Ecdf.results$ecdf <- wtd.Ecdf.results$ecdf[-1] }
# This finds the rank of each value # but note this is to index by number, not character value which would find the first of a given value via [as.character( $x)]
myindex <- findInterval(values, wtd.Ecdf.results$x)
myindex[myindex==0] <- 1 # if for some reason the minimum value doesn't match, which has occurred in testing
exact.wtd.pctile <- wtd.Ecdf.results$ecdf[ myindex ]
} else {
# **** this calculation by zone could be redone using aggregate, summarize, data.table functions etc. instead of a for loop:
exact.wtd.pctile <- vector(length=length(values))
for (z in unique(zone)) {
myvals <- values[zone==z]
mywts <- weights[zone==z]
if (all(is.na(myvals)) | all(is.na(mywts))) {
# add code here for when zone has no valid weights or no valid values due to missing values
exact.wtd.pctile[zone==z] <- NA
} else {
wtd.Ecdf.results <- Hmisc::wtd.Ecdf(myvals, weights=mywts, normwt = FALSE, type='i/n', na.rm=TRUE)
# If the first CDF estimate is greater than zero, a point (min(x),0) is placed at the beginning of the estimates.
if (length(wtd.Ecdf.results$x) == 1+ length(unique(myvals)) ) { wtd.Ecdf.results$x <- wtd.Ecdf.results$x[-1]; wtd.Ecdf.results$ecdf <- wtd.Ecdf.results$ecdf[-1] }
# This finds the rank of each value
myindex <- findInterval(myvals, wtd.Ecdf.results$x)
myindex[myindex==0] <- 1 # if for some reason the minimum value doesn't match, which has occurred in testing
exact.wtd.pctile[zone==z] <- wtd.Ecdf.results$ecdf[ myindex ]
}
}
}
return(exact.wtd.pctile)
############################################################## #
# NOTES ON THIS FUNCTION
# For documentation of wtd.Ecdf() from Hmisc package, see
# http://127.0.0.1:26624/library/Hmisc/html/wtd.stats.html
# wtd.Ecdf returns a list whose elements x and Ecdf correspond to unique sorted values of x.
#
# Min and max percentiles assigned:
# Note that if the first CDF estimate is greater than zero, a point (min(x),0) is placed at the beginning of the estimates. [so we remove that since it is just confusing]
# There will never be exactly 0 assigned as the percentile.
# The smallest that may be assigned is 1/n and this is assigned to the min input if it is unique.
# If min is not unique, all those N ties for min of n total values are assigned N/n (not 1/n) as their percentile.
# There highest percentile assigned is exactly 1.00 -- This happens to the maximum value, and for any tied for the maximum.
#
# TIES: Ties in input values are all assigned the same percentile, the percentile at the upper end of that bin's range
# so if for example the top 3 values of 100 values are tied, they are all assigned 1.000 as the percentile & the next is assigned 0.97, etc.
#
# type="i/n" to use the inverse of the empirical distribution function, using, ... wt/T,
# where wt is the cumulative weight and T is the total weight (usually total sample size).
#
# For documentation on findInterval() function:
# http://127.0.0.1:26624/library/base/html/findInterval.html
#
# By the way, for unweighted quantiles, the following would do almost the same thing as using wtd.Ecdf(x, weights=NULL) but not exactly identical:
# exact.quantile <- function(x) { Fn<-ecdf(x); Fn(x) }
#
# **** Note that this assign.pctiles() function, which relies on wtd.Ecdf(),
# will ignore NA values, and return NA as the percentile assigned to those,
# and the other percentiles assigned are among valid (non-NA) values only.
# If na.rm=TRUE (default), this version treats NA values in input by excluding them from ranking,
# making their percentile NA and finding %iles among all valid values,
# so if there were 105 values with 5 being NA and the other 100 being unique numbers,
# this function would return 1-100 as the valid %iles and return "NA" as %ile for other 5.
# For example:
# 100 * assign.pctiles(c(1001:1100, rep(NA, 39)), na.rm=FALSE)
#
# returns the following:
#
#1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
#1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046
# 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
#1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069
# 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
#1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092
# 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92
#1093 1094 1095 1096 1097 1098 1099 1100 <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA>
# 93 94 95 96 97 98 99 100 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
#<NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA>
# NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
#<NA>
# NA
#
}
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