services since April 2013. Specialist Level 1 and 2 rehabilitation
services have a mean length of stay of approximately 90 days
(SD 66) (20). The UK FIM+FAM is usually completed for each
patient within 10 days of admission and during the last week
before discharge, to evaluate the functional gains made during
the episode of care.
Sampling
L. Turner-Stokes et al.
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We extracted the cohort of all 1,956 TBI patients consecutively
admitted to the 58 Level 1 and 2 specialist neurorehabilitation
centres that submitted data to the UKROC database between
1 January 2010 and 30 May 2016, for whom a UK FIM+FAM
score was available both at admission and discharge from the
rehabilitation programme. A similar process for data extraction
and analysis was used to that in the previous publications for
stroke (12, 17), as summarized in Fig. 1.
The scores are expected to be lower (more dependent) on ad-
mission and higher (more independent) on discharge. Therefore,
to ensure the full range of the response category necessary to
evaluate reliability, and in line with previous analyses (17), we
pooled admission and discharge scores from the complete sam-
ple of n = 1,956 into a single dataset. In order not to violate the
Rasch assumption of local independence between observations,
we included only one time-point for each patient, with both
time-points equally represented. For the main dataset the random
sampling function in SPSS was used to divide the dataset into
approximately equal halves, giving 960 admission scores and
996 discharge scores. A mirror dataset was prepared using the
remaining scores (996 admission and 960 discharge scores) for
confirmatory factor analysis (CFA) of an independent sample.
Overview of analysis
The key steps were as follows:
• An initial exploratory factor analysis (EFA) was conducted on
the main dataset (n = 1,956) using the IBM Statistical Package
for Social Sciences (SPSS) v23 software. A principal compo-
nents analysis (PCA) was applied with varimax rotation. The
decision regarding the number of factors to rotate was based
on consideration of the number of factors with Eigenvalues
>1.0 and visual inspection of the scree plot.
• CFA was conducted on the mirror dataset (n = 1,956) using
the IBM Analysis of Moment Structures (AMOS) software,
which uses visual statistical software for CFA. The quality of
the model fit was assessed on 5 indices: χ 2 /df ratio, p-value,
root-mean-square error of approximation (RMSEA), the
Comparative Fit Index (CFI), the Tucker-Lewis Index (TLI)
and the Normed Fit Index (NFI). In general, excellent fit is
represented by a model where χ 2 /df <2.0, p > 0.05, RMSEA
< 0.08, CFI ≥ 0.95, TLI ≥ 0.95 and NFI ≥ 0.95. We tested the
best factor model identified in the EFA.
• Rasch analysis was conducted on the main dataset (n = 1,956)
using RUMM2030 software (23) incorporating the method
detailed below. Sample size for Rasch analysis depends on the
degree of precision required for item calibration (16). Linacre
et al. recommends a minimum sample size of 108–243, depend-
ing on how well the subjects are targeted to the scale, although
for “high stakes settings” (e.g. with assessments contributing
to clinical diagnosis) a minimum sample is recommended of
20 cases per item or 250 participants, whichever is the greater
(24). This would mean that the FIM+FAM scale would require
up to 600 cases if the intended use was for individual patient
assessment (16). However, larger datasets (n > 500) are as-
sociated with inflated χ 2 fit statistics in RUMM2030 (25, 26)
and a smaller sample size was used for the χ 2 tests of a similar
study in stroke (e.g. n = 320) (17).
Rasch analysis
Fig. 1. Summary of data sampling. Of the 1,956 consecutively admitted
traumatic brain injury (TBI) patients with complete UK Functional
Assessment Measure (UK FIM+FAM) data, admission and discharge scores
were randomly selected (using 1 time-point only for each patient) to
form the main dataset for exploratory factor analysis (EFA) and Rasch
analysis. A mirror dataset was prepared using the remaining scores
for confirmatory factor analysis of an independent sample. UKROC: UK
Rehabilitation Outcomes Collaborative; SPSS: IBM Statistical Package
for Social Sciences; confirmatory FA: confirmatory factor analysis.
www.medicaljournals.se/jrm
The most suitable type of Rasch model for the analysis was deter-
mined by the likelihood-ratio test examining the assumption of the
Rating Scale Model acting as a null hypothesis that distribution
of item thresholds across individual scale items is the same. If
the likelihood-ratio test is significant it rejects the Rating Scale
Model. Since we are examining the full scale and not specific
groups of items, there is no alternative for the unrestricted Partial
Credit Model if the Rating Scale Model is rejected. The summary
statistics of the Rasch model were assessed based on mean item
and person location, fit residual, item-trait interaction χ 2 test/p-
value. A scale with the items ideally targeted to the population has
the mean person location and the mean item location approxima-
tely at zero logits (SD 1), and item and person distributions that
mirror one another. The item-trait interaction reflects the fit of the
data to the model’s expectations; a significant p-value of < 0.05
indicates inadequate fit to the model. Reliability was estimated
using Person Separation Index (PSI). The PSI is a measure of
scale ability to discriminate between persons with different trait
levels. Its values can be interpreted similar to Cronbach’s alpha
used in classical test theory (27); values above 0.7 are required
for group use and above 0.8 for individual assessment (although
values of over 0.9 are preferred).
The Rasch analysis was carried out in 2 main analytical
pathways using the full main dataset, but, as the subjects were
found to be well-targeted to the scale (see Results section), item
trait and χ 2 tests were conducted on the reduced subset (n = 320)
to account for the effects of sample size. In the first analysis, all