We can estimate the correlations for any pair of variables using the
function reprho(), 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 string containing the name of plausible value
variables related to a construct.pv2: a string containing the name of plausible value
variables related to another construct (diferente from
the one in pv).relatedpvs: a logical value indicating if when using
two plausible value constructs, there should be related or not. If
TRUE correlations between plausible values will be
estimated in pairs (1 with 1, 2 with 2, etc.). If FALSE
correlations will be estimated using all posible combination between
both plausible value variables.rho: a string indicating the correlation coefficient to
be computed, options are "pearson" (the default),
"spearman", and "polychoric".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.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 reprho(), 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 correlation between
"item01" and "SES", we can use either of the
setups to get the overall or group results (notice that if we do not
specify the type of correlation it will default to
"pearson"):
## More than one correlation method provided. Only first method will be used (pearson).## variable1 variable2 rho se n tvalue pvalue
## 1 SES item01 -0.03101 0.01495 4483 -2.07395 0.03814## variable1 variable2 group rho se n tvalue pvalue
## 1 item01 SES Pooled -0.03101 0.01495 4483 -2.073950e+00 0.03814
## 2 item01 SES Composite -0.02555 0.01444 NA -1.769220e+00 NA
## 3 item01 SES GR1 0.01100 0.02541 1507 4.326500e-01 0.66533
## 4 item01 SES GR2 -0.01740 0.02759 1491 -6.305000e-01 0.52847
## 5 item01 SES GR3 -0.07026 0.02169 1485 -3.239700e+00 0.00122
## 6 item01 item01 Pooled 1.00000 0.00000 4483 1.335316e+15 0.00000
## 7 item01 item01 Composite 1.00000 0.00000 NA 1.860244e+15 NA
## 8 item01 item01 GR1 1.00000 0.00000 1507 1.158009e+15 0.00000
## 9 item01 item01 GR2 1.00000 0.00000 1491 8.667182e+14 0.00000
## 10 item01 item01 GR3 1.00000 0.00000 1485 1.381641e+15 0.00000
## 11 SES item01 Pooled -0.03101 0.01495 4483 -2.073950e+00 0.03814
## 12 SES item01 Composite -0.02555 0.01444 NA -1.769220e+00 NA
## 13 SES item01 GR1 0.01100 0.02541 1507 4.326500e-01 0.66533
## 14 SES item01 GR2 -0.01740 0.02759 1491 -6.305000e-01 0.52847
## 15 SES item01 GR3 -0.07026 0.02169 1485 -3.239700e+00 0.00122## variable1 variable2 group rho se n tvalue pvalue
## 1 SES item01 Pooled -0.03800 0.01641 2992 -2.31519 0.02067
## 2 SES item01 Composite -0.02963 0.01670 NA -1.77390 NA
## 3 SES item01 GR1 0.01100 0.02541 1507 0.43265 0.66533
## 4 SES item01 GR2 -0.01740 0.02759 1491 -0.63050 0.52847
## 5 SES item01 GR3 -0.07026 0.02169 1485 -3.23970 0.00122We 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.
Besides the Pearson correlation, also the Spearman correlation and
polychoric correlation can be obtained, for this we use the
rho argument:
## variable1 variable2 group rho se n tvalue pvalue
## 1 item02 item01 Pooled 0.55841 0.01523 4029 36.65308 0
## 2 item02 item01 Composite 0.55884 0.01519 NA 36.79579 NA
## 3 item02 item01 GR1 0.55507 0.02625 1344 21.14770 0
## 4 item02 item01 GR2 0.54681 0.02690 1336 20.32532 0
## 5 item02 item01 GR3 0.57464 0.02575 1349 22.31239 0## variable1 variable2 group rho se n tvalue pvalue
## 1 item02 item01 Pooled 0.60639 0.01121 4029 54.10745 0
## 2 item02 item01 Composite 0.60613 0.01127 NA 53.79030 NA
## 3 item02 item01 GR1 0.59916 0.01765 1344 33.93823 0
## 4 item02 item01 GR2 0.60349 0.02162 1336 27.91022 0
## 5 item02 item01 GR3 0.61574 0.01907 1349 32.29232 0## variable1 variable2 group rho se n tvalue pvalue
## 1 item02 item01 Pooled 0.70979 0.01237 4029 57.40152 0
## 2 item02 item01 Composite 0.71015 0.01261 NA 56.31031 NA
## 3 item02 item01 GR1 0.70916 0.02066 1344 34.31764 0
## 4 item02 item01 GR2 0.70233 0.02233 1336 31.45694 0
## 5 item02 item01 GR3 0.71897 0.02249 1349 31.96448 0We 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 correlations between more than two variables:
## variable1 variable2 group rho se n tvalue pvalue
## 1 SES item01 Pooled -0.03101 0.01495 4483 -2.07395 0.03814
## 2 SES item01 Composite -0.02555 0.01444 NA -1.76922 NA
## 3 SES item01 GR1 0.01100 0.02541 1507 0.43265 0.66533
## 4 SES item01 GR2 -0.01740 0.02759 1491 -0.63050 0.52847
## 5 SES item01 GR3 -0.07026 0.02169 1485 -3.23970 0.00122
## 6 SES item02 Pooled -0.02674 0.01481 4501 -1.80551 0.07106
## 7 SES item02 Composite -0.01879 0.01408 NA -1.33494 NA
## 8 SES item02 GR1 0.01774 0.02317 1496 0.76558 0.44405
## 9 SES item02 GR2 -0.00231 0.02877 1494 -0.08025 0.93605
## 10 SES item02 GR3 -0.07181 0.02046 1511 -3.50960 0.00046
## 11 item01 item02 Pooled 0.55841 0.01523 4029 36.65308 0.00000
## 12 item01 item02 Composite 0.55884 0.01519 NA 36.79579 NA
## 13 item01 item02 GR1 0.55507 0.02625 1344 21.14770 0.00000
## 14 item01 item02 GR2 0.54681 0.02690 1336 20.32532 0.00000
## 15 item01 item02 GR3 0.57464 0.02575 1349 22.31239 0.00000To estimate the correlations between a non plausible value variables
and a plausible value variable we need to state the normal variables in
x and plausible values variables in argument
pv:
## variable1 variable2 group rho se n tvalue pvalue
## 1 SES PVs Pooled 0.37372 0.05132 5000 7.28203 0.00000
## 2 SES PVs Composite 0.24538 0.03991 NA 6.14846 NA
## 3 SES PVs GR1 0.27224 0.07236 1667 3.76237 0.00017
## 4 SES PVs GR2 0.21660 0.06682 1666 3.24165 0.00121
## 5 SES PVs GR3 0.24730 0.06808 1667 3.63272 0.00029# More than one variable
reprho(x = c("SES","item01"),
pv = c(paste0("Math",1:5)),
setup = STGR, rho = "pearson")## variable1 variable2 group rho se n tvalue pvalue
## 1 SES PVs Pooled 0.37372 0.05132 5000 7.28203 0.00000
## 2 SES PVs Composite 0.24538 0.03991 NA 6.14846 NA
## 3 SES PVs GR1 0.27224 0.07236 1667 3.76237 0.00017
## 4 SES PVs GR2 0.21660 0.06682 1666 3.24165 0.00121
## 5 SES PVs GR3 0.24730 0.06808 1667 3.63272 0.00029
## 6 item01 PVs Pooled -0.01759 0.01840 4483 -0.95618 0.33903
## 7 item01 PVs Composite -0.00954 0.01742 NA -0.54757 NA
## 8 item01 PVs GR1 -0.01989 0.03014 1507 -0.66008 0.50931
## 9 item01 PVs GR2 -0.00214 0.03088 1491 -0.06918 0.94485
## 10 item01 PVs GR3 -0.00659 0.02948 1485 -0.22340 0.82325It is also possible to correlate two plausible value variables using
argument pv and pv2, when doing so
x should be NULL. For example, to correlate
math and reading achievement in repdata:
## group rho se n tvalue pvalue
## 1 Pooled 0.14209 0.03848 5000 3.69259 0.00022
## 2 Composite -0.14197 0.03827 NA -3.70955 NA
## 3 GR1 -0.07250 0.06419 1667 -1.12932 0.25893
## 4 GR2 -0.22991 0.07829 1666 -2.93673 0.00336
## 5 GR3 -0.12351 0.05416 1667 -2.28063 0.02270Please notice that by default reprho() assumes that both
plausible value variables are related and correlates the first plausible
value of each variable, then the seconde one of each and so on. For our
example it will estimate 5 correlations (Math1-Reading1, Math2-Reading2,
Math3-Reading3, Math4-Reading4, and Math5-Reading5) and average
them.
Nevertheless, it is also possible to calculate de correlation between
no related plausible values, therefore instead of 5 estimations,
reprho() will make 25 estimations, with all the possible
combinations between math and reading. For doing that, we can use the
argument relatedpvs=FALSE:
reprho(pv = c(paste0("Math",1:5)),
pv2 = c(paste0("Reading",1:5)),
relatedpvs = FALSE,
setup = STGR, rho = "pearson")## group rho se n tvalue pvalue
## 1 Pooled 0.15895 0.03956 5000 4.01755 0.00006
## 2 Composite -0.11932 0.03486 NA -3.42305 NA
## 3 GR1 -0.04893 0.06081 1667 -0.80465 0.42114
## 4 GR2 -0.20752 0.06326 1666 -3.28045 0.00106
## 5 GR3 -0.10153 0.05689 1667 -1.78448 0.07453When using groups we can always omit the pooled and composite calculations if we need to, by default both estimates will be calculated.
# Default
reprho(pv = paste0("Math",1:5),
pv2 = c(paste0("Reading",1:5)),
setup = STGR, rho = "pearson")## group rho se n tvalue pvalue
## 1 Pooled 0.14209 0.03848 5000 3.69259 0.00022
## 2 Composite -0.14197 0.03827 NA -3.70955 NA
## 3 GR1 -0.07250 0.06419 1667 -1.12932 0.25893
## 4 GR2 -0.22991 0.07829 1666 -2.93673 0.00336
## 5 GR3 -0.12351 0.05416 1667 -2.28063 0.02270# Only pooled
reprho(pv = paste0("Math",1:5),
pv2 = c(paste0("Reading",1:5)),
setup = STGR, rho = "pearson",
aggregates = "pooled")## group rho se n tvalue pvalue
## 1 Pooled 0.14209 0.03848 5000 3.69259 0.00022
## 2 GR1 -0.07250 0.06419 1667 -1.12932 0.25893
## 3 GR2 -0.22991 0.07829 1666 -2.93673 0.00336
## 4 GR3 -0.12351 0.05416 1667 -2.28063 0.02270# Only composite
reprho(pv = paste0("Math",1:5),
pv2 = c(paste0("Reading",1:5)),
setup = STGR, rho = "pearson",
aggregates = "composite")## group rho se n tvalue pvalue
## 1 Composite -0.14197 0.03827 NA -3.70955 NA
## 2 GR1 -0.07250 0.06419 1667 -1.12932 0.25893
## 3 GR2 -0.22991 0.07829 1666 -2.93673 0.00336
## 4 GR3 -0.12351 0.05416 1667 -2.28063 0.02270# No aggregates
reprho(pv = paste0("Math",1:5),
pv2 = c(paste0("Reading",1:5)),
setup = STGR, rho = "pearson",
aggregates = NULL)## group rho se n tvalue pvalue
## 1 GR1 -0.07250 0.06419 1667 -1.12932 0.25893
## 2 GR2 -0.22991 0.07829 1666 -2.93673 0.00336
## 3 GR3 -0.12351 0.05416 1667 -2.28063 0.02270