88
ORIGINAL ARTICLE
The Foot Posture Index: Rasch Analysis of a Novel,
Foot-Specific Outcome Measure
Anne-Maree Keenan, MAppSc, Anthony C. Redmond, PhD, Mike Horton, BSc, Philip G. Conaghan, PhD,
Alan Tennant, PhD
ABSTRACT. Keenan A-M, Redmond AC, Horton M, Conaghan PG, Tennant A. The Foot Posture Index: Rasch analysis
of a novel, foot-specific outcome measure. Arch Phys Med
Rehabil 2007;88:88-93.
Objective: To investigate the internal construct validity of a
clinician-assessed measure of foot position, the Foot Posture
Index (FPI), versions FPI-8 and FPI-6.
Design: Rasch analysis of baseline FPI scores from studies
conducted during the development of the instrument.
Setting: A community-based and a hospital-based study,
conducted at 2 institutions.
Participants: Measures were obtained from 143 participants
(98 men, 45 women; age range, 8 – 65y).
Interventions: Not applicable.
Main Outcome Measures: Rasch analysis was undertaken
using RUMM2020 software in order to evaluate the following
properties of the FPI: unidimensionality of each item included
in the FPI, the differential item functioning (DIF) of each item,
and item and person separation indices.
Results: In the developmental draft of the instrument, the
8-item FPI-8 showed some misfit to the Rasch model (␹216
test⫽27.63, P⫽.03), indicating lack of unidimensionality. Two
items were identified as problematic in the Rasch modeling:
Achilles’ tendon insertion (Helbing’s sign), which showed
illogical response ordering and “congruence of the lateral border of the foot,” which showed misfit, indicating that this item
may be measuring a different construct (␹22 test⫽15.35, P⬍.01).
All FPI-8 items showed an absence of DIF, and the person
separation index (PSI) was good (PSI⫽.88). The revised FPI-6,
which does not include the 2 problematic items, showed unidimensionality (␹212 test⫽11.49, P⫽.49), indicating a good
overall fit to the model, and improvement over the preliminary
version. With the removal of the 2 problematic items, there
were no disordered thresholds; all items remained DIF free and
all individual items displayed a good fit to the model. The
person-separation index for the FPI was similar for both the
8-item (FPI-8⫽.880) and 6-item (FPI-6⫽.884) versions.
Conclusions: The original FPI-8 showed significant mismatching to the model. The 2 items in the FPI-8 that were
identified as problematic in clinical validation studies were also
found to be contributing to the lack of fit to the Rasch model.
The finalized 6-item instrument showed good metric proper-
From the Academic Unit of Musculoskeletal Disease, University of Leeds, Leeds, UK.
Presented in part to Health Outcomes 2005: Making a Difference, August 17–18,
2005, Canberra, Australia, and the British Society for Rheumatology, May 17–18,
2006, Glasgow, Scotland.
No commercial party having a direct financial interest in the results of the research
supporting this article has or will confer a benefit upon the authors or upon any
organization with which the authors are associated.
Reprint requests to Anne-Maree Keenan, MAppSc, Academic Unit of Musculoskeletal Disease, University of Leeds, Chapel Allerton Hospital, Chapeltown Rd,
Leeds, LS7 4SA, United Kingdom, e-mail: a.keenan@leeds.ac.uk.
0003-9993/07/8801-10886$32.00/0
doi:10.1016/j.apmr.2006.10.005
Arch Phys Med Rehabil Vol 88, January 2007
ties, including good individual item fit and good overall fit to
the model, along with a lack of differential item functioning.
This analysis provides further evidence for the validity of the
FPI-6 as a clinical instrument for use in screening studies and
shows that it has the potential to be analyzed using parametric
strategies.
Key Words: Foot; Rehabilitation; Treatment outcome.
© 2007 by the American Congress of Rehabilitation Medicine and the American Academy of Physical Medicine and
Rehabilitation
HE FOOT POSTURE INDEX (FPI) is a novel, footspecific outcome measure that was developed in order to
T
quantify variation in the position of the foot easily and quickly
in a clinical setting. It is particularly intended for large sample
studies where complex instrumented assessment (eg, gait laboratory assessment) is impractical or unnecessary. It has already been used in studies of risk factors for injury in athletes
and naval recruits, treatment of plantar heel pain, and response
to orthotic therapy in different foot types.1-5 The original draft
of the FPI was based on clinician assessment of 8 characteristics of foot posture (a version known as the FPI-8) but after
further validity and reliability investigations, the authors have
suggested that the FPI-8 be reduced to a 6-item measure, the
FPI-6.6 While the clinical validity and reliability of the FPI
have been established,6-8 modern psychometric properties, such
as unidimensionality and discriminatory ability, have yet to be
determined.
Foot Posture Index
The FPI was developed in response to a commonly expressed need for better foot measures9-13 due to the absence of
a widely accepted or adequately validated method for quantifying variation in foot posture in the clinical setting.14 The FPI
consists of a series of criterion-based observations that combine to provide a quantification of postural variation in 3 major
regions of the foot (rearfoot, midfoot, forefoot) in the 3 cardinal
body planes. The scoring system uses a 5-point Likert-type
scale where lower scores represent a more supinated foot
position and higher scores a more pronated position. The
original version of the FPI used 8 component scores (table 1)
and demonstrated reasonable interrater and test-retest reliability across a number of patient populations.1,2,7
The original FPI-8 also demonstrated good construct validity6 when compared with the valgus index (a standing measure
of foot position commonly used in research but cumbersome to
use in a clinical setting),15,16 but only moderate concurrent
validity measured against plain film radiographs.8 Item reduction based on a series of validation studies6 yielded a final
6-item version of the index, the FPI-6 (see table 1), which
demonstrated good concurrent validity against a static lowerlimb kinematic model derived from an electromagnetic motion
tracking system. Reliability is enhanced in the finalized version, and the capacity to predict dynamic foot postures during
gait has been demonstrated to be better than for other clinical
89
FOOT POSTURE INDEX, Keenan
Table 1: Individual Item Tests of Fit for the FPI-8 Items
Item
Item Difficulty (logits)
SE
Fit Res
␹2 Test
df
P
Talar head palpation
Curves above and below lateral malleoli
Inversion and eversion of the calcaneus
Bulge in the region of the TNJ
Congruence of the medial longitudinal arch
Abduction and adduction of the forefoot on the rear foot (too-many-toes)
Congruence of the lateral border of the foot
Helbing’s sign (curve of the Achilles’ tendon)
⫺1.24
1.05
⫺0.48
0.70
⫺1.01
1.68
⫺0.43
⫺0.27
.16
.17
.13
.16
.19
.15
.18
.19
0.89
1.20
0.05
⫺1.28
⫺1.68
⫺1.41
1.88
0.72
2.00
1.02
1.01
2.91
3.19
1.83
15.35
0.32
2
2
2
2
2
2
2
2
.37
.60
.60
.23
.20
.40
⬍.01
.85
NOTE. Location refers to the location the item is along the metric ruler, the standard error (SE) of the measure, and fit residuals (Fit Res), or
how well each item relates to the overall model. A significant chi-square test indicates that an item does not fit the model.
Abbreviation: TNJ, talo-navicular joint.
measures.6 Further validation using modern psychometric standards17 provides valuable information about the performance
characteristics and suitability of the measure to various methodologic applications.
Rasch Analysis
Rasch analysis is a probabilistic mathematical modeling
technique used to assess properties of outcome measures including unidimensionality (the extent to which items measure
a single construct), item difficulty (the relative difficulty of the
items when compared to one another), and person separation
(the extent to which items distinguish between distinct levels of
functioning). Rasch analysis has been widely used in the development and validation of a number of outcome measures.17-20
The Rasch model is the current standard for the development
of unidimensional scales (eg, of impairment or quality of life)
delivering metric quality outcomes in health care.21 Data collected from ordinal questionnaires or scales, which are intended to be summated into an overall score, are tested against
the expectations of this measurement model. The model defines
the ideal item response characteristics if measurement (at the
interval level) is to be achieved. The observed response patterns achieved are tested against expected patterns (a probabilistic form of Guttman scaling),22 and a variety of fit statistics
determine whether fit is adequate to the model.23
Within the framework of Rasch measurement, the scale
should work the same way, irrespective of the group being
assessed (eg, items should behave similarly independent of age,
sex, or disease characteristics).24 If, at the same overall level of
impairment, groups do not display the same probability of
affirming the item, then the item is deemed to display differential item functioning (DIF), thus violating the requirement of
unidimensionality.25
Finally, Rasch modeling also transforms ordinal scores obtained by summing scores from each item into interval measures.26 Transformed scores (as logit values) form an internally
valid and unidimensional measure that may be considered for
parametric statistical analysis, which enables calculation of
information such as percentage change, mean scores, and other
values that cannot otherwise be expressed appropriately for
ordinal data.27
The aim of this study was to assess the unidimensionality
and DIF of the original FPI-8 and the finalized FPI-6 using
Rasch analysis techniques.
METHODS
Data Capture
In the first analysis, we captured FPI data from 143 people
(98 men, 45 women) with a range of foot types, comprising 2
groups of participants involved in a series of validation experiments.6 Participants were either patients with Charcot-MarieTooth disease (n⫽12; 7 men, 5 women; age range, 8 – 63y) or
healthy adults participating in a prospective injury study
(n⫽131; 91 men, 40 women; age range, 18 – 65y). Ethics
approval was granted by the university review boards of the
University of Western Sydney, the University of Sydney, and
the Children’s Hospital at Westmead in Sydney, as appropriate
to the study site. All participants provided informed consent.
Patients were assessed using all 8 items described in the original FPI and total scores were derived for both FPI-8 and FPI-6.
Once the initial analyses of the FPI data to the Rasch model
was finalized, we transformed the FPI scores to Rasch scores.
The transformation of the raw FPI scores to Rasch scores is
undertaken in order to change data that are ordinal in nature to
Rasch transformed, interval scores. For the generation of transformed scores, large data sets are required; to undertake this
transformation, a second data set (n⫽426) was used. This
second data set included participants on whom demographic
information (including sex and age) was not captured. As such,
this data could not be included in the primary Rasch analysis,
because assessment of DIF, a key aspect within the Rasch
model, could not be included. Rasch analysis was repeated on
the extended data set, prior to the transformation of the scores.
We entered the data into both SPSSa and RUMM2020 software packages28,b using a Rasch partial credit model as the
basis of analysis.29 Data were rescaled (⫹1 to ⫹5) to eliminate
the negative numerals employed in the clinical scoring system
(⫺2 to ⫹2). In the first instance, FPI-8 data was analyzed to
evaluate initial fit of the data, threshold ordering and DIF.
Re-analysis was then undertaken using the data from the modified FPI-6.
General Tests of Fit
To determine how the FPI fits the Rasch unidimensional
model, we used a series of fit statistics. Item-trait interaction
quantifies the fit of the observed data to the predicted model.
This statistic, represented by the chi-square value, reflects the
degree of invariance of each of the items and how they function
together, so it represents how the items function across the 1
trait (or construct). A significant chi-square indicates that there
are problems with fit of all the items: that is, that the score is
not unidimensional. All of the items should assess the same (or
a single) construct. For the FPI, each item included should be
assessing foot posture; items should not be assessing muscle
strength, flexibility, or range of motion.
A further test to explore the unidimensionality of the instrument is to look at the residual fit statistics. The residuals are the
standardized person-item differences between the observed
data and what is expected by the model for every person’s
Arch Phys Med Rehabil Vol 88, January 2007
90
FOOT POSTURE INDEX, Keenan
response to every item. Because it is standardized, a perfect fit
to the model would give a mean of zero and a standard
deviation (SD) of 1 when summed over all items.30
Associated with the residual fit statistics, further evidence to
support unidimensionality can be gathered by evaluating patterns in the residuals using principal components analysis of
the fit residuals. The aim of this evaluation is to identify
patterns of the residuals once the “Rasch factor” has been
extracted. This is important in order to identify any subsets of
items that may be loading together. The absence of any meaningful pattern in the residuals will be deemed to support the
assumption of local independence of the items, where the
response of 1 item is not conditional on the response of
another.30 If any patterns are identified in the residuals, the
significance of the pattern can be tested by comparing the
person ability estimates (where one would expect the individual to score along the Rasch scale) generated from any subset
of items that have been identified as loading together, to the
person ability estimates generated from the entire item set. The
person ability estimates are then compared via independent
t tests. If less than 5% of the independent t tests are shown to
be significant, then the assumption of local independence is
supported.26
As well as considering unidimensionality, the fit statistics
also consider the stability of the instrument, irrespective of the
group being evaluated. While groups may be expected to have
different foot postures (eg, women may have a slightly different FPI score than men; or people with Charcot-Marie-Tooth
disease may have lower scores than those without), their group
membership at any given level of the trait should not influence
how they are scored. This type of analysis is referred to as DIF
and is identified by a 2-way analysis of variance of the residuals31 with statistical significance indicating the presence of
differential item functioning and, hence, compromise to the
unidimensionality of the scale.
Components should cover a range of less extreme and extreme characteristics (difficulty or severity) coherently. This is
referred to as item difficulty or hierarchy and is expressed as a
logit value, the natural logarithm of the odds of a person being
able to perform a certain task.18 The hierarchy in the FPI scores
relates to representation of the range of foot postures—from the
most supinated through neutral to pronated foot types. The item
difficulty reflects the internal construct validity of measure with
the theoretical ordering of each of the items.
The ability of the scale to discriminate among different
groups of such patients is determined by the person separation
index (PSI). Values above 0.7 indicate the ability to identify at
Fig 1. Person-item threshold
distribution for the FPI-8.
Arch Phys Med Rehabil Vol 88, January 2007
least 2 groups of patients.32 The PSI in the Rasch model is
analogous to the Cronbach ␣; 0.7 is considered a minimal value
for group use and .85 for individual patient use.33
RESULTS
The FPI-8
The initial overall item-trait interaction of the original FPI-8
indicated that some misfit to the Rasch model was apparent
within the data (␹216 test⫽27.63, P⫽.03). The residual mean
value for the items was .05, with an SD of 1.35. A significant
item-trait interaction indicated that some items of foot positioning were not measuring in a consistent manner among
discrete groups of people with differing foot postures. An
analysis of the threshold ordering indicated that one of the
items (Helbing’s sign) displayed disordered thresholds, meaning that the scoring response categories did not follow the
expected ordering. All other 7 items displayed appropriately
ordered thresholds. Given this fundamental lack of fit to the
model, detailed principal components analysis of the fit residuals was not examined for the FPI-8.
Further analysis of individual items indicated that the fit of
another item, congruence of the lateral border of the foot, was
also problematic (␹22 test⫽15.35, P⫽.01) and appeared to be
measuring a separate dimension not related to the overall FPI.
The misfit indicates that there was a lack of the expected
probabilistic relationship between this particular item and the
other items in the FPI-8.
The possibility of sex differences in FPI rating was explored
by analysis of DIF with Bonferroni adjustments for multiple
comparisons. All items on the FPI-8 were DIF free, indicating
a lack of bias associated with sex. A summary table of the
individual item separation and tests of fit is presented in table 1.
The person item threshold map is represented in figure 1.
The distribution of the items indicated that range of difficulty
covered by the items was comprehensive. The items were at
least 0.1 standard errors (SEs) apart (see table 1), indicating
appropriate discrimination between foot types.
The person-fit separation index for the FPI-8 of .88 and the
Cronbach ␣ of .86 indicating that there was good internal
consistency with the measure.
The FPI-6
To investigate whether the validation process and subsequent refinement of the instrument had improved its internal
construct validity, Rasch analysis was performed on the final-
91
FOOT POSTURE INDEX, Keenan
Table 2: Individual Item Tests of Fit for the FPI-6 Items
Item
Item Difficulty (logits)
SE
Fit Res
␹2 Test
df
P
Talar head palpation
Curves above and below lateral malleoli
Inversion and eversion of the calcaneus
Bulge in the region of the TNJ
Congruence of the medial longitudinal arch
Abduction and adduction of the forefoot on the rear foot (too-many-toes)
⫺1.64
0.98
0.53
⫺1.25
1.68
⫺0.30
.16
.18
.17
.20
.16
.21
0.26
1.55
⫺0.91
⫺1.29
⫺0.86
1.33
0.87
3.32
3.35
1.90
0.80
1.25
2
2
2
2
2
2
.65
.19
.19
.39
.67
.54
NOTE. Location refers to the location the item is along the metric ruler, the SE of the measure, and fit residuals, or how well each item relates
to the overall model. A significant chi-square test indicates that an item does not fit the model.
ized FPI-6. Of note, the 2 items that had been removed following the clinical validation process (the lateral border of the
foot and Helbing’s sign) were the same items that had proved
problematic in the Rasch analysis of the FPI-8. Re-analysis
using the data from the 6-item version of the FPI showed good
item-trait interaction (␹212 test⫽11.49, P⫽.49), indicating a
good overall fit to the model. The residual mean value for the
items was .012, with an SD of 1.22. With the removal of the 2
problematic items, there were no disordered thresholds, all
items remained DIF free and all individual items displayed a
good fit to the model, in terms of chi-square probability and fit
residuals (table 2).
A principal components analysis of the residuals indicated
that the first component accounted for 27.84% of the variance,
thus supporting the notion that the scale is unidimensional.
Furthermore, the person frequency distribution (fig 2) demonstrated that there was a large measurement range of the item
thresholds in the FPI-6 and indicated that the measure was able
to discriminate across different foot positions.
Testing of the local dependency of the items once the FPI-6
was put through the Rasch model indicated that there was a
minor pattern in the residuals; items associated with rearfoot
measurement (frontal plane motion of the calcaneus; talar head
palpation and curvature of the malleoli) loaded in 1 direction,
while items associated with the midfoot (sustentaculum tali,
medial longitudinal arch and adduction, abduction of the forefoot)
loaded in the other direction. Person estimates were generated
from the 2 subsets of items identified, and these were compared
with the person estimates generated from the entire item set.
The differences were proved to be trivial, however, and not
statistically significant for any of the independent t tests exploring differences between the FPI-6 and the midfoot or
rearfoot subscales.
As with the FPI-8 analysis, all items on the FPI-6 were DIF
free, indicating no sex differences in FPI measurements.
Assessment of the item difficulty indicated that the distribution of the items indicated that range of difficulty covered by
the items was comprehensive. The items are again at least .15
SE apart, indicating increased discrimination between foot
types compared with the FPI-8.
As with the FPI-8, the person-fit separation of the FPI-6 was
good, with the PSI of .88 and the Cronbach ␣ of .87 indicating
that there was good internal consistency with the measure.
Transformation Scores for the FPI-6
Rasch analysis of the extended data set demonstrated good
fit to the model (␹232 test⫽46.7, P⫽.11). Person location data
was transformed and mapped onto raw FPI-6 scores. A transformation table is presented in table 3, which lists the transformation values from raw FPI scores to the Rasch transformed
logit values.
DISCUSSION
The FPI was designed to provide an objective measure of
foot posture quickly and easily in a clinical setting. While the
validation and reliability of the FPI has been described previously, the aim of the current study was to describe in detail the
internal construct validity of the FPI and to explore the fit of the
data to the latest statistical models. Our results indicated that
while the original FPI-8 demonstrated good internal consistency and may be of some clinical use, the data did not fit the
Rasch model. Two items demonstrated poor metric properties—Helbing’s sign and the congruence of the lateral border of
the foot— both of which were also identified as problematic in
the clinical validation studies. Helbing’s sign demonstrated a
Fig 2. Person-item threshold
distribution for the FPI-6.
Arch Phys Med Rehabil Vol 88, January 2007
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FOOT POSTURE INDEX, Keenan
Table 3: Conversion of Raw FPI-6 Scores to Rasch
Transformed Scores
FPI-6 Raw Score
Transformed Score
⫺12
⫺11
⫺10
⫺9
⫺8
⫺7
⫺6
⫺5
⫺4
⫺3
⫺2
⫺1
0
1
2
3
4
5
6
7
8
9
10
11
12
⫺10.47
⫺7.96
⫺6.45
⫺5.54
⫺4.84
⫺4.25
⫺3.71
⫺3.20
⫺2.67
⫺2.12
⫺1.54
⫺0.91
⫺0.21
0.50
1.16
1.75
2.33
2.98
3.81
4.83
5.68
6.36
7.01
7.77
8.65
NOTE. Calculations derived from data (n⫽426) that included those
data in the Rasch analysis (n⫽143) and additional data from 2 other
studies (n⫽283) not included in the detailed Rasch analysis due to
inadequate clinical detail for evaluation of DIF.
lack of discrimination in the extreme range, with very few of
the 143 participants demonstrating lateral bowing of the Achilles’ tendon. Furthermore, there was some inappropriate ordering of the scores on the scale of this item indicating apparent
difficulty in identifying degrees of difference. The lateral border of the foot criterion demonstrated significant mismatching
to the model. It appeared that this item was not reflective of
overall foot posture and was measuring a different construct,
perhaps associated with foot shape or size.
The removal of the 2 items and reanalysis of the finalized
FPI-6 addressed these issues, supporting the validity of the
FPI-6 as a unidimensional measure. The FPI-6 demonstrated
good metric properties, including good individual item fit and
good overall fit to the Rasch model, along with a lack of
differential item functioning.
While the FPI was originally developed as an ordinal measure, the results of the Rasch modeling of the FPI-6 indicate
that summative FPI-6 score can be mapped satisfactorily to a
linear metric. Metric mapping of the FPI-6 total scores assists
in the use of the FPI-6 as a research tool: with appropriate
assessment of raw FPI data and transformation of raw scores
through the Rasch measurement model there is potential for
employing parametric statistical analyses in studies using the
FPI-6. Using the Rasch transformed score (see table 3) allows
better consideration of clinically important outcomes, including percentage change scores and smallest detectable differences. Furthermore, if appropriate to a study design, transformed scores have the potential to be used to establish
appropriate numbers for powering a study.
While the results of this study validate the internal construct
validity of the FPI-6, 2 limitations must also be acknowledged.
Arch Phys Med Rehabil Vol 88, January 2007
First, it must be noted that the study used 2 groups co-opted
from other studies; 1 group with known neuromuscular disease
and a second healthy group. DIF was not found for sex but it
is possible that in other applications, factors not investigated
here may demonstrate DIF. This warrants further study in
specific target groups. Furthermore, the sample size used is
moderately large for a clinical validation study but is relatively
small for Rasch analysis and this may affect the precision of the
estimates of the Rasch model. A large scale study is still
required to establish normative values for FPI-6 scores and it
would be appropriate to confirm the findings of the current
Rasch analysis in a larger sample. Finally, in all the data
collected, including those for the transformation scores, there
were no extreme values recorded at either end of the scale.
While this may reflect the true clinical picture, in that it is
unlikely to see such pronated or supinated cases, the values of
the extreme estimates in the logit transformation are therefore
not true values but extrapolated from the modeling available
within RUMM2020.
CONCLUSIONS
The original FPI-8 demonstrated limitations in its internal
construct validity, with 2 of the items (Helbing’s sign, congruence of the lateral border of the foot) demonstrating significant
mismatching to the model. The removal of these 2 items
following the clinical validation phase has addressed these
issues. The finalized FPI-6 demonstrated good internal construct validity including good individual item fit and good
overall fit to the model, along with a lack of DIF. The FPI-6
raw scores can be converted to Rasch transformed scores,
thereby allowing data generated to be used as interval data.
This serves as evidence that the FPI-6 is a unidimensional
measure of foot posture and may be suited to a range of clinical
applications.
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