We can estimate the arithmetic mean of any variable using the
function repmean(), as any other “rep” function of
ILSAstats, we need to specify the data (df),
the total weights (wt), the replicate weights
(repwt), and the method (method).
Besides these basic options, other arguments can be used:
x: a string with the name of the variable (or
variables) to be used in the analysis.PV: a logical value indicating if x are
plausible values or not. If FALSE the statistics of each
variable will be computed independently. If TRUE all
variables in x will be treated as plausible values of the
same construct, and all their statistics will be combined.var: a string of length 1 indicating the type of
variance to be estimated. Options are "unbiased" or
"ML".group: a string containing the name of the variable
that contains the groups of countries. If used all statistics will be
estimated separately for each group, and groups will be treated as
independent from each other, e.g., countries.by: a string containing the name of a second grouping
variable. If used, all statistics will be estimated separately for each
category, and categories will be treated as
non-independent from each other, e.g., boys and
girls.exclude: a string containing which groups should be
excluded from aggregate estimations.aggregates: a string containing the aggregate
statistics that should be estimated. Options include:
"pooled" for also estimating all groups (without
exclusions) as a single group; and "composite" for
averaging all the estimations for each single group (without
exclusions).For repmean(), first we need to create the replicate
weights. Using the included repdata data, and using the
"LANA" method:
To make it easier to specify some arguments, it is advised that we
create also a "repsetup" object. We will create three
setups for this example: one without groups, one with groups and without
exclusions, and one with groups and exclusions (excluding group 2):
# No groups
STNG <- repsetup(repwt = RW, wt = "wt", df = repdata, method = "LANA")
# With groups
STGR <- repsetup(repwt = RW, wt = "wt", df = repdata, method = "LANA",
group = "GROUP")
# With groups and exclusions
STGE <- repsetup(repwt = RW, wt = "wt", df = repdata, method = "LANA",
group = "GROUP", exclude = "GR2")For example, if we want to estimate the mean of variable
"SES", we can use either of the setups to get the overall
or group results:
## N mean se sd sdse var varse
## 1 5000 49.96674 0.01442 1.00784 0.008 1.01574 0.01613## group N mean se sd sdse var varse
## 1 Pooled 5000 49.96674 0.01442 1.00784 0.00800 1.01574 0.01613
## 2 Composite NA 49.96646 0.01221 0.93833 0.00926 0.88046 0.01739
## 3 GR1 1667 49.52108 0.02037 0.93659 0.01468 0.87720 0.02750
## 4 GR2 1666 49.95496 0.01965 0.93962 0.01700 0.88289 0.03195
## 5 GR3 1667 50.42334 0.02325 0.93878 0.01636 0.88130 0.03072## group N mean se sd sdse var varse
## 1 Pooled 3334 49.97266 0.01717 1.04050 0.01099 1.08263 0.02287
## 2 Composite NA 49.97221 0.01546 0.93768 0.01099 0.87925 0.02062
## 3 GR1 1667 49.52108 0.02037 0.93659 0.01468 0.87720 0.02750
## 4 GR2 1666 49.95496 0.01965 0.93962 0.01700 0.88289 0.03195
## 5 GR3 1667 50.42334 0.02325 0.93878 0.01636 0.88130 0.03072We can notice that using no groups we would get the same results for the pooled estimates if we use groups and no exclusions. But, when we exclude group 2, the pooled and the composite estimate changes.
We can also estimate multiple variables at once, for example
"SES" and "Math1":
## variable N mean se sd sdse var varse
## 1 SES 5000 49.96674 0.01442 1.00784 0.00800 1.01574 0.01613
## 2 Math1 5000 0.00191 0.01718 1.02336 0.00928 1.04726 0.01899## variable group N mean se sd sdse var varse
## 1 SES Pooled 5000 49.96674 0.01442 1.00784 0.00800 1.01574 0.01613
## 2 SES Composite NA 49.96646 0.01221 0.93833 0.00926 0.88046 0.01739
## 3 SES GR1 1667 49.52108 0.02037 0.93659 0.01468 0.87720 0.02750
## 4 SES GR2 1666 49.95496 0.01965 0.93962 0.01700 0.88289 0.03195
## 5 SES GR3 1667 50.42334 0.02325 0.93878 0.01636 0.88130 0.03072
## 6 Math1 Pooled 5000 0.00191 0.01718 1.02336 0.00928 1.04726 0.01899
## 7 Math1 Composite NA 0.00149 0.01283 0.89950 0.00852 0.80920 0.01532
## 8 Math1 GR1 1667 -0.60164 0.02192 0.90847 0.01330 0.82532 0.02417
## 9 Math1 GR2 1666 0.01102 0.02382 0.88556 0.01502 0.78422 0.02660
## 10 Math1 GR3 1667 0.59510 0.02080 0.90446 0.01583 0.81805 0.02864When treating with plausible values, we need to specify the names of
all plausible values of a construct, and use the argument
"PV" so all estimates will be combined (if not all
variables will be estimated separately). For example, for estimating the
mean achievement in math for this sample we would use:
## N mean se sd sdse var varse
## 1 5000 0.00524 0.01634 1.02282 0.01099 1.04619 0.02247## group N mean se sd sdse var varse
## 1 Pooled 5000 0.00524 0.01634 1.02282 0.01099 1.04619 0.02247
## 2 Composite NA 0.00482 0.01970 0.90173 0.01192 0.81329 0.02150
## 3 GR1 1667 -0.59327 0.03943 0.90148 0.02093 0.81283 0.03766
## 4 GR2 1666 0.01857 0.02395 0.89383 0.02075 0.79905 0.03708
## 5 GR3 1667 0.58917 0.03693 0.90989 0.02028 0.82799 0.03699When using groups we can always omit the pooled and composite calculations if we need to, by default both estimates will be calculated.
## group N mean se sd sdse var varse
## 1 Pooled 5000 0.00524 0.01634 1.02282 0.01099 1.04619 0.02247
## 2 Composite NA 0.00482 0.01970 0.90173 0.01192 0.81329 0.02150
## 3 GR1 1667 -0.59327 0.03943 0.90148 0.02093 0.81283 0.03766
## 4 GR2 1666 0.01857 0.02395 0.89383 0.02075 0.79905 0.03708
## 5 GR3 1667 0.58917 0.03693 0.90989 0.02028 0.82799 0.03699## group N mean se sd sdse var varse
## 1 Pooled 5000 0.00524 0.01634 1.02282 0.01099 1.04619 0.02247
## 2 GR1 1667 -0.59327 0.03943 0.90148 0.02093 0.81283 0.03766
## 3 GR2 1666 0.01857 0.02395 0.89383 0.02075 0.79905 0.03708
## 4 GR3 1667 0.58917 0.03693 0.90989 0.02028 0.82799 0.03699## group N mean se sd sdse var varse
## 1 Composite NA 0.00482 0.01970 0.90173 0.01192 0.81329 0.02150
## 2 GR1 1667 -0.59327 0.03943 0.90148 0.02093 0.81283 0.03766
## 3 GR2 1666 0.01857 0.02395 0.89383 0.02075 0.79905 0.03708
## 4 GR3 1667 0.58917 0.03693 0.90989 0.02028 0.82799 0.03699## group N mean se sd sdse var varse
## 1 GR1 1667 -0.59327 0.03943 0.90148 0.02093 0.81283 0.03766
## 2 GR2 1666 0.01857 0.02395 0.89383 0.02075 0.79905 0.03708
## 3 GR3 1667 0.58917 0.03693 0.90989 0.02028 0.82799 0.03699For estimating the mean of not-independent groups, we can use the
argument by. For example, for estimating the mean
achievement in math between GENDER==0 and
GENDER==1, we can:
## $ALL
## N mean se sd sdse var varse
## 1 5000 0.00524 0.01634 1.02282 0.01099 1.04619 0.02247
##
## $`GENDER==0`
## N mean se sd sdse var varse mean_1 meandiff_1
## 1 2483 0.45427 0.03749 0.93268 0.0166 0.86999 0.03097 -0.43552 0.88979
## meandiffse_1 tvalue_1 df_1 pvalue_1
## 1 0.079 11.26338 4998 0
##
## $`GENDER==1`
## N mean se sd sdse var varse mean_0 meandiff_0
## 1 2517 -0.43552 0.04587 0.90835 0.02226 0.82533 0.04067 0.45427 -0.88979
## meandiffse_0 tvalue_0 df_0 pvalue_0
## 1 0.079 -11.26338 4998 0This will provide us with the overall statistics, the statistics for
each category within GENDER, and statistics of the
difference between means between all categories.
Of course, we can also estimate this using groups:
## $ALL
## group N mean se sd sdse var varse
## 1 GR1 1667 -0.59327 0.03943 0.90148 0.02093 0.81283 0.03766
## 2 GR2 1666 0.01857 0.02395 0.89383 0.02075 0.79905 0.03708
## 3 GR3 1667 0.58917 0.03693 0.90989 0.02028 0.82799 0.03699
##
## $`GENDER==0`
## group N mean se sd sdse var varse mean_1
## 1 GR1 819 -0.17761 0.04462 0.79348 0.03070 0.62996 0.04868 -0.99226
## 2 GR2 846 0.48279 0.03513 0.78112 0.03694 0.61083 0.05735 -0.45673
## 3 GR3 818 1.05458 0.06162 0.78595 0.03401 0.61826 0.05327 0.14141
## meandiff_1 meandiffse_1 tvalue_1 df_1 pvalue_1
## 1 0.81465 0.09313 8.74764 1665 0
## 2 0.93952 0.07148 13.14385 1664 0
## 3 0.91317 0.08944 10.20971 1665 0
##
## $`GENDER==1`
## group N mean se sd sdse var varse mean_0
## 1 GR1 848 -0.99226 0.07126 0.81277 0.03932 0.66135 0.06357 -0.17761
## 2 GR2 820 -0.45673 0.04786 0.73724 0.03835 0.54426 0.05668 0.48279
## 3 GR3 849 0.14141 0.05126 0.78658 0.03239 0.61908 0.05123 1.05458
## meandiff_0 meandiffse_0 tvalue_0 df_0 pvalue_0
## 1 -0.81465 0.09313 -8.74764 1665 0
## 2 -0.93952 0.07148 -13.14385 1664 0
## 3 -0.91317 0.08944 -10.20971 1665 0For estimating the mean of independent groups, we can use the
argument repmeandif(). The only argument of this function
will be an object produced by repmean (using or not using
by):
m1 <- repmean(x = paste0("Math",1:5), PV = TRUE, setup = STGR, aggregates = NULL,
by = NULL)
m2 <- repmean(x = paste0("Math",1:5), PV = TRUE, setup = STGR, aggregates = NULL,
by = "GENDER")## group1 group2 dif se tvalue df pvalue
## 1 GR1 GR1 0.00000 0.05576 0.00000 3332 1
## 2 GR1 GR2 -0.61185 0.04614 -13.26073 3331 0
## 3 GR1 GR3 -1.18245 0.05402 -21.88912 3332 0
## 4 GR2 GR1 0.61185 0.04614 13.26073 3331 0
## 5 GR2 GR2 0.00000 0.03388 0.00000 3330 1
## 6 GR2 GR3 -0.57060 0.04401 -12.96524 3331 0
## 7 GR3 GR1 1.18245 0.05402 21.88912 3332 0
## 8 GR3 GR2 0.57060 0.04401 12.96524 3331 0
## 9 GR3 GR3 0.00000 0.05222 0.00000 3332 1## $ALL
## group1 group2 dif se tvalue df pvalue
## 1 GR1 GR1 0.00000 0.05576 0.00000 3332 1
## 2 GR1 GR2 -0.61185 0.04614 -13.26073 3331 0
## 3 GR1 GR3 -1.18245 0.05402 -21.88912 3332 0
## 4 GR2 GR1 0.61185 0.04614 13.26073 3331 0
## 5 GR2 GR2 0.00000 0.03388 0.00000 3330 1
## 6 GR2 GR3 -0.57060 0.04401 -12.96524 3331 0
## 7 GR3 GR1 1.18245 0.05402 21.88912 3332 0
## 8 GR3 GR2 0.57060 0.04401 12.96524 3331 0
## 9 GR3 GR3 0.00000 0.05222 0.00000 3332 1
##
## $`GENDER==0`
## group1 group2 dif se tvalue df pvalue
## 1 GR1 GR1 0.00000 0.06310 0.00000 1636 1
## 2 GR1 GR2 -0.66040 0.05679 -11.62881 1663 0
## 3 GR1 GR3 -1.23219 0.07608 -16.19598 1635 0
## 4 GR2 GR1 0.66040 0.05679 11.62881 1663 0
## 5 GR2 GR2 0.00000 0.04968 0.00000 1690 1
## 6 GR2 GR3 -0.57180 0.07093 -8.06147 1662 0
## 7 GR3 GR1 1.23219 0.07608 16.19598 1635 0
## 8 GR3 GR2 0.57180 0.07093 8.06147 1662 0
## 9 GR3 GR3 0.00000 0.08715 0.00000 1634 1
##
## $`GENDER==1`
## group1 group2 dif se tvalue df pvalue
## 1 GR1 GR1 0.00000 0.10078 0.00000 1694 1
## 2 GR1 GR2 -0.53552 0.08584 -6.23858 1666 0
## 3 GR1 GR3 -1.13367 0.08778 -12.91490 1695 0
## 4 GR2 GR1 0.53552 0.08584 6.23858 1666 0
## 5 GR2 GR2 0.00000 0.06768 0.00000 1638 1
## 6 GR2 GR3 -0.59814 0.07013 -8.52902 1667 0
## 7 GR3 GR1 1.13367 0.08778 12.91490 1695 0
## 8 GR3 GR2 0.59814 0.07013 8.52902 1667 0
## 9 GR3 GR3 0.00000 0.07249 0.00000 1696 1Some ILSAs use confidence intervals instead of point estimates for
means. For adding confidence intervals to an object produced by
repmean(), we can use repmeanCI(), selecting a
confidence level (by default it is 0.05):
## group N mean se CIdown CIup sd sdse var varse
## 1 GR1 1667 -0.59327 0.03943 -0.67056 -0.51599 0.90148 0.02093 0.81283 0.03766
## 2 GR2 1666 0.01857 0.02395 -0.02838 0.06552 0.89383 0.02075 0.79905 0.03708
## 3 GR3 1667 0.58917 0.03693 0.51680 0.66155 0.90989 0.02028 0.82799 0.03699## $ALL
## group N mean se CIdown CIup sd sdse var varse
## 1 GR1 1667 -0.59327 0.03943 -0.67056 -0.51599 0.90148 0.02093 0.81283 0.03766
## 2 GR2 1666 0.01857 0.02395 -0.02838 0.06552 0.89383 0.02075 0.79905 0.03708
## 3 GR3 1667 0.58917 0.03693 0.51680 0.66155 0.90989 0.02028 0.82799 0.03699
##
## $`GENDER==0`
## group N mean se CIdown CIup sd sdse var varse
## 1 GR1 819 -0.17761 0.04462 -0.26505 -0.09016 0.79348 0.03070 0.62996 0.04868
## 2 GR2 846 0.48279 0.03513 0.41394 0.55164 0.78112 0.03694 0.61083 0.05735
## 3 GR3 818 1.05458 0.06162 0.93380 1.17537 0.78595 0.03401 0.61826 0.05327
## mean_1 meandiff_1 meandiffse_1 tvalue_1 df_1 pvalue_1
## 1 -0.99226 0.81465 0.09313 8.74764 1665 0
## 2 -0.45673 0.93952 0.07148 13.14385 1664 0
## 3 0.14141 0.91317 0.08944 10.20971 1665 0
##
## $`GENDER==1`
## group N mean se CIdown CIup sd sdse var varse
## 1 GR1 848 -0.99226 0.07126 -1.13193 -0.85259 0.81277 0.03932 0.66135 0.06357
## 2 GR2 820 -0.45673 0.04786 -0.55053 -0.36294 0.73724 0.03835 0.54426 0.05668
## 3 GR3 849 0.14141 0.05126 0.04094 0.24187 0.78658 0.03239 0.61908 0.05123
## mean_0 meandiff_0 meandiffse_0 tvalue_0 df_0 pvalue_0
## 1 -0.17761 -0.81465 0.09313 -8.74764 1665 0
## 2 0.48279 -0.93952 0.07148 -13.14385 1664 0
## 3 1.05458 -0.91317 0.08944 -10.20971 1665 0We can also not add the confidence intervals, just obtain them separately:
## group CIdown CIup
## 1 GR1 -0.67056 -0.51599
## 2 GR2 -0.02838 0.06552
## 3 GR3 0.51680 0.66155