1. Overview
Although the circumplex package is capable of analyzing and
visualizing data in a “source-agnostic” manner (i.e., without knowing
what the numbers correspond to), it can be helpful to both the user and
the package to have more contextual information about which
instrument/questionnaire the data come from. For example, knowing the
specific instrument used can enable the package to automatically score
item-level responses and standardize these scores using normative data.
Furthermore, a centralized repository of information about circumplex
instruments would provide a convenient and accessible way for users to
discover and begin using new instruments. To address these needs, a
suite of new instrument-related functions (and underlying data to power
them) was added to the circumplex package in version 0.2.0.
Section 2, “Loading and Examining Instrument Objects”, shows how to
preview the instruments in the circumplex package. It shows how to load
the information about one instrument for use in analysis. It also shows
how to extract general and specific information about that instrument.
The following functions will be discussed: instruments(),
print(), summary(), scales(),
items(), anchors(), norms(), and
View().
Section 3, “Instrument-related Tidying Functions”, shows how to use
the information about an instrument to transform and summarize
circumplex data. It will demonstrate how to ipsatize item-level
responses (i.e., apply deviation scoring across variables), how to
calculate scale scores from item-level responses (with or without
imputing/prorating missing values), and how to standardize scale scores
using normative/comparison data. The following functions will be
discussed: ipsatize(), score(), and
norm_standardize(). The Wrap-up lists what the page covered
and names the next page to read.
2. Loading and Examining Instrument Objects
Previewing the available instruments
Our goal is to eventually include all circumplex instruments in this
package. However, due to time-constraints and copyright issues, this
goal may be delayed or even impossible to fully realize. However, you
can always preview the list of currently available instruments using the
instruments() function. This function will print the
abbreviation, name, and (in parentheses) the “code” for each available
instrument. We will return to the code in the next section.
instruments()
#> The circumplex package currently includes 15 instruments:
#> 1. CAIS: Child and Adolescent Interpersonal Survey (cais)
#> 2. CSIE: Circumplex Scales of Interpersonal Efficacy (csie)
#> 3. CSIG: Circumplex Scales of Intergroup Goals (csig)
#> 4. CSIP: Circumplex Scales of Interpersonal Problems (csip)
#> 5. CSIV: Circumplex Scales of Interpersonal Values (csiv)
#> 6. IEI: Interpersonal Emotion Inventory (iei)
#> 7. IGI-CR: Interpersonal Goals Inventory for Children, Revised Version (igicr)
#> 8. IIP-32: Inventory of Interpersonal Problems, Brief Version (iip32)
#> 9. IIP-64: Inventory of Interpersonal Problems (iip64)
#> 10. IIP-SC: Inventory of Interpersonal Problems Short Circumplex (iipsc)
#> 11. IIS-32: Inventory of Interpersonal Strengths, Brief Version (iis32)
#> 12. IIS-64: Inventory of Interpersonal Strengths (iis64)
#> 13. IIT-C: Inventory of Influence Tactics Circumplex (iitc)
#> 14. IPIP-IPC: IPIP Interpersonal Circumplex (ipipipc)
#> 15. ISC: Interpersonal Sensitivities Circumplex (isc)
If there are additional circumplex instruments you would like to have
added to the package (especially if you are the
author/copyright-holder), please contact me. Note that some information
(e.g., item text and normative data) may not be available for all
instruments due to copyright issues. However, many instruments are
released as open-access and have full item text and normative data
included in the package.
Loading a specific instrument
Instrument information is loaded into R’s memory when the circumplex
package is loaded. We can just refer to each by “code,” such as the
csip code for the Circumplex Scales of Interpersonal
Problems. The code is an object in R’s environment, so do not put it in
quotes.
csip
#> CSIP: Circumplex Scales of Interpersonal Problems
#> 64 items, 8 scales, 1 normative data sets
#> Boudreaux, Ozer, Oltmanns, & Wright (2018)
#> <https://doi.org/10.1037/pas0000505>
Examining an instrument in-depth
To examine the information available about a loaded instrument, there
are several options. To print a long list of formatted information about
the instrument, use the summary() function. This will
return information about the instrument’s scales, rating scale anchors,
items, and normative data set(s). The summary of each instrument is also
available from the package reference
page.
summary(ipipipc)
#> IPIP-IPC: IPIP Interpersonal Circumplex
#> 32 items, 8 scales, 1 normative data sets
#> Markey & Markey (2009)
#> <https://doi.org/10.1177/1073191109340382>
#>
#> The IPIP-IPC contains 8 circumplex scales.
#> PA: Assured-Dominant (90 degrees)
#> BC: Arrogant-Calculating (135 degrees)
#> DE: Cold-Hearted (180 degrees)
#> FG: Aloof-Introverted (225 degrees)
#> HI: Unassured-Submissive (270 degrees)
#> JK: Unassuming-Ingenuous (315 degrees)
#> LM: Warm-Agreeable (360 degrees)
#> NO: Gregarious-Extraverted (45 degrees)
#>
#> The IPIP-IPC is rated using the following 5-point scale.
#> 1. Very Inaccurate
#> 2. Moderately Inaccurate
#> 3. Neither Inaccurate nor Accurate
#> 4. Moderately Accurate
#> 5. Very Accurate
#>
#> The IPIP-IPC contains 32 items (open-access):
#> 1. Am quiet around strangers
#> 2. Speak softly
#> 3. Tolerate a lot from others
#> 4. Am interested in people
#> 5. Feel comfortable around people
#> 6. Demand to be the center of interest
#> 7. Cut others to pieces
#> 8. Believe people should fend for themselves
#> 9. Am a very private person
#> 10. Let others finish what they are saying
#> 11. Take things as they come
#> 12. Reassure others
#> 13. Start conversations
#> 14. Do most of the talking
#> 15. Contradict others
#> 16. Don't fall for sob stories
#> 17. Don't talk a lot
#> 18. Seldom toot my own horn
#> 19. Think of others first
#> 20. Inquire about others' well-being
#> 21. Talk to a lot of different people at parties
#> 22. Speak loudly
#> 23. Snap at people
#> 24. Don't put a lot of thought into things
#> 25. Have little to say
#> 26. Dislike being the center of attention
#> 27. Seldom stretch the truth
#> 28. Get along well with others
#> 29. Love large parties
#> 30. Demand attention
#> 31. Have a sharp tongue
#> 32. Am not interested in other people's problems
#>
#> The IPIP-IPC currently has 1 normative data set(s):
#> 1. 274 American college students
#> Reference kind: no identified source
#> Norms source unconfirmed; instrument published as Markey & Markey (2009)
#> <https://doi.org/10.1177/1073191109340382>
Specific subsections of this output can be returned individually
using the scales(), anchors(),
items(), and norms() functions. These
functions are especially useful when you need to know a specific bit of
information about an instrument and don’t want the console to be flooded
with unneeded information.
anchors(ipipipc)
#> The IPIP-IPC is rated using the following 5-point scale.
#> 1. Very Inaccurate
#> 2. Moderately Inaccurate
#> 3. Neither Inaccurate nor Accurate
#> 4. Moderately Accurate
#> 5. Very Accurate
norms(ipipipc)
#> The IPIP-IPC currently has 1 normative data set(s):
#> 1. 274 American college students
#> Reference kind: no identified source
#> Norms source unconfirmed; instrument published as Markey & Markey (2009)
#> <https://doi.org/10.1177/1073191109340382>
Some of these functions also have additional arguments to customize
their output. For instance, the scales() function has the
items argument, which will display the items for each scale
when set to TRUE.
scales(ipipipc, items = TRUE)
#> The IPIP-IPC contains 8 circumplex scales.
#> PA: Assured-Dominant (90 degrees)
#> 6. Demand to be the center of interest
#> 14. Do most of the talking
#> 22. Speak loudly
#> 30. Demand attention
#> BC: Arrogant-Calculating (135 degrees)
#> 7. Cut others to pieces
#> 15. Contradict others
#> 23. Snap at people
#> 31. Have a sharp tongue
#> DE: Cold-Hearted (180 degrees)
#> 8. Believe people should fend for themselves
#> 16. Don't fall for sob stories
#> 24. Don't put a lot of thought into things
#> 32. Am not interested in other people's problems
#> FG: Aloof-Introverted (225 degrees)
#> 1. Am quiet around strangers
#> 9. Am a very private person
#> 17. Don't talk a lot
#> 25. Have little to say
#> HI: Unassured-Submissive (270 degrees)
#> 2. Speak softly
#> 10. Let others finish what they are saying
#> 18. Seldom toot my own horn
#> 26. Dislike being the center of attention
#> JK: Unassuming-Ingenuous (315 degrees)
#> 3. Tolerate a lot from others
#> 11. Take things as they come
#> 19. Think of others first
#> 27. Seldom stretch the truth
#> LM: Warm-Agreeable (360 degrees)
#> 4. Am interested in people
#> 12. Reassure others
#> 20. Inquire about others' well-being
#> 28. Get along well with others
#> NO: Gregarious-Extraverted (45 degrees)
#> 5. Feel comfortable around people
#> 13. Start conversations
#> 21. Talk to a lot of different people at parties
#> 29. Love large parties
3. Instrument-related Tidying Functions
It is a good idea in practice to digitize and save each participant’s
response to each item on an instrument, rather than just their scores on
each scale. Having access to item-level data will make it easier to spot
and correct mistakes, will enable more advanced analysis of missing
data, and will enable latent variable models that account for
measurement error (e.g., structural equation modeling). Furthermore, the
functions described below will make it easy to transform and summarize
such item-level data into scale scores.
First, however, we need to make sure the item-level data is in the
expected format. Your data should be stored in a data frame where each
row corresponds to one observation (e.g., participant, organization, or
timepoint) and each column corresponds to one variable describing these
observations (e.g., item responses, demographic characteristics, scale
scores). The tidyverse packages
provide excellent tools for getting your data into this format from a
variety of different file types and formats.
For the purpose of illustration, we will work with a small-scale data
set, which includes item-level responses to the Inventory of
Interpersonal Problems, Short Circumplex (IIP-SC) for just 10
participants. As will become important later on, this data set contains
a small amount of missing values (represented as NA). This
data set is included as part of the circumplex package and can be
previewed as follows:
raw_iipsc
#> IIP01 IIP02 IIP03 IIP04 IIP05 IIP06 IIP07 IIP08 IIP09 IIP10 IIP11 IIP12
#> 1 0 0 0 0 1 0 1 0 2 1 0 0
#> 2 1 1 0 0 3 2 2 1 0 1 0 1
#> 3 1 0 1 0 1 1 1 3 0 1 0 0
#> 4 3 2 3 NA 2 3 2 3 2 3 2 4
#> 5 0 0 0 1 0 0 1 1 0 1 0 2
#> 6 0 0 0 0 0 0 1 1 0 0 0 0
#> 7 1 0 0 0 2 1 1 0 1 0 0 0
#> 8 1 0 1 0 1 1 2 1 1 0 0 0
#> 9 0 0 2 2 0 1 3 0 1 0 1 1
#> 10 0 0 0 0 0 0 2 0 0 0 0 0
#> IIP13 IIP14 IIP15 IIP16 IIP17 IIP18 IIP19 IIP20 IIP21 IIP22 IIP23 IIP24
#> 1 0 1 4 3 2 4 2 0 1 0 0 0
#> 2 4 3 3 1 0 0 1 0 1 2 0 0
#> 3 2 3 3 2 2 1 1 0 3 2 3 1
#> 4 2 1 2 3 1 2 2 1 3 2 3 2
#> 5 1 1 3 1 0 1 0 1 1 0 1 1
#> 6 0 0 2 1 1 0 0 0 0 0 1 1
#> 7 1 1 1 0 1 0 0 0 0 1 1 1
#> 8 1 NA 2 1 1 0 1 0 0 0 1 1
#> 9 0 2 2 2 1 2 2 0 0 0 3 0
#> 10 0 2 2 1 0 0 0 0 0 0 0 0
#> IIP25 IIP26 IIP27 IIP28 IIP29 IIP30 IIP31 IIP32
#> 1 3 3 3 0 0 0 1 0
#> 2 0 0 0 1 0 0 0 2
#> 3 1 1 1 0 3 2 3 2
#> 4 1 2 3 2 3 2 3 2
#> 5 2 1 0 0 0 0 0 0
#> 6 0 0 0 0 0 0 0 1
#> 7 1 0 0 0 1 1 0 0
#> 8 1 1 1 0 0 1 2 1
#> 9 1 0 1 0 0 1 3 0
#> 10 0 0 0 0 0 0 0 0
Ipsatizing item-level data
For some forms of circumplex data analysis (e.g., analysis of
circumplex fit) but not others (e.g., structural summary method), it can
be helpful to transform item-level responses by subtracting each
participant’s mean across all items from his or her response on each
item. This practice is called “ipsatizing” or, more precisely, deviation
scoring across variables. This practice will attenuate the general
factor across all items and recasts the item-level responses as
deviations from one’s own mean rather than absolute responses. To
perform ipsatizing and create a new set of ipsatized responses to each
item, use the ipsatize() function.
ips_iipsc <- ipsatize(data = raw_iipsc, items = 1:32, append = FALSE)
print(ips_iipsc)
#> IIP01_i IIP02_i IIP03_i IIP04_i IIP05_i IIP06_i
#> 1 -1.0000000 -1.0000000 -1.0000000 -1.0000000 0.0000000 -1.0000000
#> 2 0.0625000 0.0625000 -0.9375000 -0.9375000 2.0625000 1.0625000
#> 3 -0.4062500 -1.4062500 -0.4062500 -1.4062500 -0.4062500 -0.4062500
#> 4 0.7096774 -0.2903226 0.7096774 NA -0.2903226 0.7096774
#> 5 -0.6250000 -0.6250000 -0.6250000 0.3750000 -0.6250000 -0.6250000
#> 6 -0.2812500 -0.2812500 -0.2812500 -0.2812500 -0.2812500 -0.2812500
#> 7 0.5000000 -0.5000000 -0.5000000 -0.5000000 1.5000000 0.5000000
#> 8 0.2580645 -0.7419355 0.2580645 -0.7419355 0.2580645 0.2580645
#> 9 -0.9687500 -0.9687500 1.0312500 1.0312500 -0.9687500 0.0312500
#> 10 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500
#> IIP07_i IIP08_i IIP09_i IIP10_i IIP11_i IIP12_i
#> 1 0.0000000 -1.0000000 1.0000000 0.0000000 -1.0000000 -1.0000000
#> 2 1.0625000 0.0625000 -0.9375000 0.0625000 -0.9375000 0.0625000
#> 3 -0.4062500 1.5937500 -1.4062500 -0.4062500 -1.4062500 -1.4062500
#> 4 -0.2903226 0.7096774 -0.2903226 0.7096774 -0.2903226 1.7096774
#> 5 0.3750000 0.3750000 -0.6250000 0.3750000 -0.6250000 1.3750000
#> 6 0.7187500 0.7187500 -0.2812500 -0.2812500 -0.2812500 -0.2812500
#> 7 0.5000000 -0.5000000 0.5000000 -0.5000000 -0.5000000 -0.5000000
#> 8 1.2580645 0.2580645 0.2580645 -0.7419355 -0.7419355 -0.7419355
#> 9 2.0312500 -0.9687500 0.0312500 -0.9687500 0.0312500 0.0312500
#> 10 1.7812500 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500
#> IIP13_i IIP14_i IIP15_i IIP16_i IIP17_i IIP18_i
#> 1 -1.0000000 0.000000 3.0000000 2.0000000 1.0000000 3.0000000
#> 2 3.0625000 2.062500 2.0625000 0.0625000 -0.9375000 -0.9375000
#> 3 0.5937500 1.593750 1.5937500 0.5937500 0.5937500 -0.4062500
#> 4 -0.2903226 -1.290323 -0.2903226 0.7096774 -1.2903226 -0.2903226
#> 5 0.3750000 0.375000 2.3750000 0.3750000 -0.6250000 0.3750000
#> 6 -0.2812500 -0.281250 1.7187500 0.7187500 0.7187500 -0.2812500
#> 7 0.5000000 0.500000 0.5000000 -0.5000000 0.5000000 -0.5000000
#> 8 0.2580645 NA 1.2580645 0.2580645 0.2580645 -0.7419355
#> 9 -0.9687500 1.031250 1.0312500 1.0312500 0.0312500 1.0312500
#> 10 -0.2187500 1.781250 1.7812500 0.7812500 -0.2187500 -0.2187500
#> IIP19_i IIP20_i IIP21_i IIP22_i IIP23_i IIP24_i
#> 1 1.0000000 -1.0000000 0.0000000 -1.0000000 -1.0000000 -1.0000000
#> 2 0.0625000 -0.9375000 0.0625000 1.0625000 -0.9375000 -0.9375000
#> 3 -0.4062500 -1.4062500 1.5937500 0.5937500 1.5937500 -0.4062500
#> 4 -0.2903226 -1.2903226 0.7096774 -0.2903226 0.7096774 -0.2903226
#> 5 -0.6250000 0.3750000 0.3750000 -0.6250000 0.3750000 0.3750000
#> 6 -0.2812500 -0.2812500 -0.2812500 -0.2812500 0.7187500 0.7187500
#> 7 -0.5000000 -0.5000000 -0.5000000 0.5000000 0.5000000 0.5000000
#> 8 0.2580645 -0.7419355 -0.7419355 -0.7419355 0.2580645 0.2580645
#> 9 1.0312500 -0.9687500 -0.9687500 -0.9687500 2.0312500 -0.9687500
#> 10 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500
#> IIP25_i IIP26_i IIP27_i IIP28_i IIP29_i IIP30_i
#> 1 2.0000000 2.0000000 2.0000000 -1.0000000 -1.0000000 -1.0000000
#> 2 -0.9375000 -0.9375000 -0.9375000 0.0625000 -0.9375000 -0.9375000
#> 3 -0.4062500 -0.4062500 -0.4062500 -1.4062500 1.5937500 0.5937500
#> 4 -1.2903226 -0.2903226 0.7096774 -0.2903226 0.7096774 -0.2903226
#> 5 1.3750000 0.3750000 -0.6250000 -0.6250000 -0.6250000 -0.6250000
#> 6 -0.2812500 -0.2812500 -0.2812500 -0.2812500 -0.2812500 -0.2812500
#> 7 0.5000000 -0.5000000 -0.5000000 -0.5000000 0.5000000 0.5000000
#> 8 0.2580645 0.2580645 0.2580645 -0.7419355 -0.7419355 0.2580645
#> 9 0.0312500 -0.9687500 0.0312500 -0.9687500 -0.9687500 0.0312500
#> 10 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500 -0.2187500
#> IIP31_i IIP32_i
#> 1 0.0000000 -1.0000000
#> 2 -0.9375000 1.0625000
#> 3 1.5937500 0.5937500
#> 4 0.7096774 -0.2903226
#> 5 -0.6250000 -0.6250000
#> 6 -0.2812500 0.7187500
#> 7 -0.5000000 -0.5000000
#> 8 1.2580645 0.2580645
#> 9 2.0312500 -0.9687500
#> 10 -0.2187500 -0.2187500
Above, we told the function to take all the variables from column 1
to column 32 and calculate new ipsatized variables ending in
_i (although different prefixes and
suffixes can be used). By default, the mean for each
observation/row is calculated after ignoring any missing values, but we
could have changed this by adding na.rm = FALSE. By setting
append to FALSE, only the ipsatized versions are returned,
but if we changed this to TRUE then the original variables would have
been included as well.
We can check that the ipsatization was successful by calculating the
mean of each row (i.e., each participant’s mean response) in the
original and ipsatized data frames. We do this below using the
rowMeans() function; we also apply the round()
function to make the results fit on one row. As expected, we find below
that the mean of each participant is zero in the ipsatized data frame
but not in the original.
round(rowMeans(raw_iipsc, na.rm = TRUE), 2)
#> [1] 1.00 0.94 1.41 2.29 0.62 0.28 0.50 0.74 0.97 0.22
round(rowMeans(ips_iipsc, na.rm = TRUE), 2)
#> [1] 0 0 0 0 0 0 0 0 0 0
Scoring item-level data
For many forms of circumplex data analysis (e.g., structural summary
method), it can be very helpful to summarize item-level responses by
calculating scale scores. This is typically done by averaging a set of
items that all measure the same underlying construct (e.g., location in
the circumplex model). For example, the IIP-SC has 32 items in total
that measure 8 scales representing octants of the interpersonal
circumplex model. Thus, a participant’s score on each scale is
calculated as the arithmetic mean of his or her responses to four
specific items. Using the aggregate of multiple similar items produces
scale scores with higher reliability than would be achieved by using
only a single item per scale.
scales(iipsc)
#> The IIP-SC contains 8 circumplex scales.
#> PA: Domineering (90 degrees)
#> BC: Vindictive (135 degrees)
#> DE: Cold (180 degrees)
#> FG: Socially Avoidant (225 degrees)
#> HI: Nonassertive (270 degrees)
#> JK: Exploitable (315 degrees)
#> LM: Overly Nurturant (360 degrees)
#> NO: Intrusive (45 degrees)
Although calculating the arithmetic mean of a handful of items is not
terribly difficult mathematically, doing so manually (e.g., by hand)
across multiple scales and multiple participants can be tedious and
error-prone. To address these issues, the circumplex package offers the
score() function, which automatically calculates scale
scores from item-level data.
To demonstrate, let’s return to the raw_iipsc data set.
We need to give the score() function a data frame
containing the item-level data (i.e., the data set), a list of variables
from that data frame that contain the item-level responses to be scored,
and an instrument object containing instructions on how to score the
data. In order for scoring to work properly, the list of items
must be in ascending order from the first to the last item and the
ordering of the items must be the same as that assumed by the
package. Be sure to check your item numbers against those
displayed by the items() function, especially if you
shuffle your items.
scale_scores <- score(
data = raw_iipsc,
items = 1:32,
instrument = iipsc,
append = FALSE
)
print(scale_scores)
#> PA BC DE FG HI JK LM NO
#> 1 1.75 2.00 1.25 0.000000 0.50 0.2500000 1.50 0.75
#> 2 0.25 0.50 0.25 0.500000 2.00 1.7500000 1.25 1.00
#> 3 1.00 0.75 0.75 0.000000 2.25 2.0000000 2.50 2.00
#> 4 1.75 2.25 2.50 2.333333 2.50 2.0000000 2.50 2.50
#> 5 0.50 0.75 0.00 1.000000 0.50 0.2500000 1.25 0.75
#> 6 0.25 0.00 0.00 0.000000 0.00 0.0000000 1.00 1.00
#> 7 1.00 0.00 0.00 0.000000 1.00 1.0000000 0.75 0.25
#> 8 1.00 0.25 0.75 0.000000 0.50 0.6666667 1.75 1.00
#> 9 0.75 0.50 1.50 0.750000 0.00 1.0000000 2.75 0.50
#> 10 0.00 0.00 0.00 0.000000 0.00 0.5000000 1.00 0.25
Because we set append to FALSE, the
scale_scores data frame contains only the scale score
variables. These were named using the scale abbreviations shown by the
scales() function (i.e., two-letter abbreviations from PA
to NO). You can customize the naming of these variables by using the
prefix and suffix arguments (e.g., to make
them IIP_PA to IIP_NO).
Note that the na.rm argument for the
score() function defaulted to TRUE, which
means that missing values were ignored in calculating the scale scores.
This practice is common in the literature, but is technically a form of
single imputation and thus can produce biased results when data are not
missing completely at random (MCAR). Please examine and report the
amount and patterns of missingness in your data.
Standardizing scale-level data
Finally, it can often be helpful to transform scale-level data
through reference to a reference sample: a specific group of
people whose scores on the same instrument the package ships as a table
of means and standard deviations. This is often called “norm
standardizing” and involves subtracting the reference sample’s mean
score on a scale from each participant’s score on that scale and then
dividing this difference by the reference sample’s standard deviation.
This rescales the scale scores to be in standard deviation units and to
describe the magnitude of each participant’s difference from the average
of that particular sample.
For many circumplex instruments, the data needed to perform
standardization is included in its instrument object. Some instruments
have more than one reference sample — for example, separate samples for
men and women, or for children and adults. In selecting a reference
sample, the first question to ask is which group your participants are
most sensibly described relative to; the size of the sample is a
secondary consideration.
Before choosing, it is worth knowing what these reference samples
generally are.
The counts below come from the sample descriptions in the
Norms element of every instrument object the package ships.
(The code that gathers and counts them is omitted.)
The package ships 23 reference samples across 15 instruments. 10 of
them describe college or undergraduate students, and 6 have fewer than
300 participants. Most are the single study sample that was available to
the researchers who published the instrument — people recruited at one
institution, at one time — rather than a group assembled to represent
any wider population. The exception is the IIP-32 and IIP-64, whose 6
samples come from a national standardization study designed for exactly
that purpose. At the other end, 2 of the tables are published in no
source that has been identified, and scores standardized against them
rest on unverified numbers. You do not have to work any of this out from
the descriptions: every sample carries a Kind —
standardization, published, or
unsourced — which is where the two counts just given come
from, and which norms() prints and
norm_standardize() names in the message it prints unless
you silence it. A reference sample is therefore best read as a concrete,
described group of people to compare against, and the
Population column printed below names the group each sample
was drawn from rather than a population the sample stands in for.
To demonstrate, let’s examine the reference samples available for the
IIP-SC. Below we see two options: a sample of American college students
and a sample of American psychiatric outpatients. They differ greatly in
size, but what makes one or the other the right choice is which group
your participants resemble.
norms(iipsc)
#> The IIP-SC currently has 2 normative data set(s):
#> 1. 872 American college students
#> Reference kind: identified published source
#> Hopwood, Pincus, DeMoor, & Koonce (2008)
#> <https://doi.org/10.1080/00223890802388665>
#> 2. 106 American psychiatric outpatients
#> Reference kind: identified published source
#> Soldz, Budman, Demby, & Merry (1995)
#> <https://doi.org/10.1177/1073191195002001006>
Assuming our example data also come from a non-psychiatric community
sample of mostly college students, the first reference sample is the
better choice — because it describes a similar group of people, not
because it is larger. Which sample you choose matters a great deal more
than how precisely that sample’s mean and standard deviation are
estimated: switching to a different reference sample typically shifts
standardized scores by several times the uncertainty that even the
smallest shipped sample contributes. If your participants were
psychiatric outpatients, the second sample would be the appropriate
reference despite its size.
To transform the scale scores we calculated during the last section,
we can call the norm_standardize() function and give it the
scale_scores object we created above. We will save the
output of this function to a data frame named z_scales to
reflect the idea that standardized scores are often called
“z-scores.”
z_scales <- norm_standardize(
data = scale_scores,
scales = 1:8,
instrument = iipsc,
sample = 1,
append = FALSE
)
#> Standardized against IIP-SC normative sample 1: N = 872, American college students. Reference kind: identified published source. 1 other sample is available; see norms().
print(z_scales)
#> PA_z BC_z DE_z FG_z HI_z JK_z
#> 1 1.50000000 1.7500000 0.4093567 -1.10554090 -1.0054645 -1.3313783
#> 2 -0.77272727 -0.4239130 -0.7602339 -0.57783641 0.6338798 0.4281525
#> 3 0.36363636 -0.0615942 -0.1754386 -1.10554090 0.9071038 0.7214076
#> 4 1.50000000 2.1123188 1.8713450 1.35708004 1.1803279 0.7214076
#> 5 -0.39393939 -0.0615942 -1.0526316 -0.05013193 -1.0054645 -1.3313783
#> 6 -0.77272727 -1.1485507 -1.0526316 -1.10554090 -1.5519126 -1.6246334
#> 7 0.36363636 -1.1485507 -1.0526316 -1.10554090 -0.4590164 -0.4516129
#> 8 0.36363636 -0.7862319 -0.1754386 -1.10554090 -1.0054645 -0.8426197
#> 9 -0.01515152 -0.4239130 0.7017544 -0.31398417 -1.5519126 -0.4516129
#> 10 -1.15151515 -1.1485507 -1.0526316 -1.10554090 -1.5519126 -1.0381232
#> LM_z NO_z
#> 1 0.04242424 -0.34375
#> 2 -0.26060606 -0.03125
#> 3 1.25454545 1.21875
#> 4 1.25454545 1.84375
#> 5 -0.26060606 -0.34375
#> 6 -0.56363636 -0.03125
#> 7 -0.86666667 -0.96875
#> 8 0.34545455 -0.03125
#> 9 1.55757576 -0.65625
#> 10 -0.56363636 -0.96875
Again, because we set append to FALSE, the output
contains only the norm standardized scale-level variables. The new
variables are named the same as the scale score variables except with a
configurable prefix and suffix (by default,
they are given only a suffix of _z). These variables are
the ones we are most likely to use in subsequent analyses (e.g., the
structural summary method).
Wrap-up
In this vignette, we learned how to preview the instruments available
in the circumplex package, load and examine the information contained in
one of these instrument objects, ipsatize item-level data, calculate
scale scores from item-level data, and standardize those scale scores
using normative data included in the package. We are now in an excellent
position to discover and implement new circumplex instruments. The next
page to read is “Introduction to SSM Analysis”, which analyzes scores
like the ones these tools produce.
Special thanks to the authors and publishers who granted permission
to include information about their instruments in this package: Chloe
Bliton, Michael Boudreaux, Robert Hatcher, Christopher Hopwood, Leonard
Horowitz, Kenneth Locke, Patrick Markey, Aaron Pincus, Elisa Trucco, and
MindGarden Inc.