Dimensionality and item-difficulty hierarchy of the lower-extremity Fugl-Meyer assessment in individuals with sub-acute and chronic stroke

Abstract

Objective

To investigate the dimensionality and item-difficulty hierarchy of the lower extremity section of the Fugl-Meyer assessment (FMA-LE).

Design

Secondary analyses of data pooled from four existing datasets: a Phase III randomized controlled trial investigating the effectiveness of body weight support and a treadmill for rehabilitation of walking post-stroke and three cross-sectional studies investigating the link between impaired motor performance post-stroke and walking.

Setting

University research centers and rehabilitation centers.

Participants

A pooled sample of 535 individuals with a stroke (age = 61.91 ± 12.42 years; male = 313).

Interventions

Not applicable.

Main Outcome Measure(s)

Confirmatory factor analyses (CFA) and Rasch residual Principal component analysis (PCA) investigated the dimensionality of the FMA-LE. The Rasch analysis rating scale model (RSM) investigated item-difficulty hierarchy of the FMA-LE.

Results

The CFA showed adequate fit of a three-factor model with 2/3 indices (CFA = 0.95; TLI = 0.94; RMSEA = 0.124) showing good model fit. Rasch PCA showed that removal of the reflex and coordination items explained 90.8% of variance in the data, suggesting that the abnormal synergy items contributed to the measurement of a unidimensional construct. However, RSM results revealed deviations in the item-difficulty hierarchy of the unidimensional abnormal synergy items from the originally proposed stepwise sequence of motor recovery.

Conclusion(s)

Our findings suggest that the FMA-LE might represent a multidimensional construct challenging the use of a total score of the FMA-LE to predict lower extremity motor recovery. Removal of the misfit items resulted in creation of a unidimensional scale comprised of the abnormal synergy items. However, this unidimensional scale deviates from the originally proposed hierarchical ordering.

The Fugl-Meyer Assessment of the lower extremity (FMA-LE) is a widely used impairment-based outcome measure used to evaluate LE motor recovery and predict functional recovery in individuals with stroke.^1–4 The psychometric properties of the FMA-LE have been extensively tested using classical testing methods and the scale has shown good validity,^4–8 excellent reliability^9,10 and internal consistency.¹¹ However classical test methods investigate the assessment as a whole, whereas contemporary testing methods (e.g. item response theory, IRT) evaluate the item-level psychometric properties. The need for an item level analysis is apparent when examining the construct underlying the FMA-LE.

Twitchell and Brunnstrom established the conceptual framework that underlies the FMA-LE.^12,13 Motor recovery of the LE was characterized to progress through a stepwise predictable sequence, from initial flaccid paralysis, to recovery of reflex activity, to the development of stereotypical synergistic voluntary movement and finally to the restoration of normal movement.^12,13 The FMA-LE consists of 17 items arranged in a hierarchy (from reflex items, synergy items and coordination items), paralleling the hypothesized stepwise sequential recovery process. A total summed score of the 17 items is currently used in rehabilitation research trials to represent the level of LE motor recovery. However, the rationale for computation of a total score is lacking.

Reflex, abnormal synergistic movements and coordination items of the FMA-LE measure more than one construct of motor control and recovery. Summing the responses from distinct constructs of a multidimensional assessment obscures what the total score might represent. Reflexes are simple and automatic responses to sensory stimulation that are physiologically controlled at lower levels of the central nervous system.¹⁴ Contrary to automatic reflexive movements, voluntary movements after a stroke described as abnormal synergy patterns (“within synergy”, “combining synergy” and “out of synergy”) in the FMA-LE selectively represent the voluntary control of isolated movement likely to be controlled at the cortical level (e.g., motor cortex).¹⁴ Lastly, the process of recovery for LE gross coordination (“speed”, “dysmetria” and “tremor”) is likely to be controlled at both cortical and sub-cortical levels (e.g., cerebellum and basal ganglia),¹⁴ suggesting that the recovery process of coordination may physiologically differ compared to reflexive behaviors and abnormal synergy movements. Therefore, it can be argued that the construct underlying FMA-LE is multidimensional, capturing at least three different aspects of motor control and recovery, including (a) involuntary reflexive behaviors, (b) voluntary movements (represented as moving within, combining and out of synergy patterns), hereby referred to as ‘abnormal synergy’ movements and (c) gross coordination.

Rasch analysis, an IRT based methodology, offers the advantage of testing dimensionality and item-level psychometric properties of the scale as opposed to testing the instrument as a whole (using total scores).¹⁵ In addition, Rasch analysis allows an investigation of the item-difficulty hierarchy of the scale. Earlier studies have used IRT methodologies to evaluate the FMA.^16,17 For instance, a Rasch based short form was developed from the total FMA comprising of upper and lower extremities.¹⁶ A computerized adaptive test (CAT) of the FMA has also been developed comprising of both upper and lower extremity items.¹⁷ Since the lower-extremity items cannot be selectively administered from the CAT, the application of the relevant FMA-LE items in rehabilitation trials focused on LE recovery is limited.

This study aimed to systematically investigate the dimensionality, item-difficulty hierarchy and item-level measurement properties of the FMA-LE using Rasch analysis. We hypothesized that the FMA-LE comprises three different constructs of reflex, abnormal synergy movements and gross coordination, and that the item-difficulty hierarchy will deviate from the originally proposed stepwise progression of motor recovery.

METHODS

Participants

Retrospective data pooled from four rehabilitation studies^18–21 were analyzed (on-line only appendix). All participants gave their informed consent before participation and the study protocols were approved by the institutional review boards at the respective institutions.

Instrumentation

Trained physical therapists administered the FMA-LE using standardized testing procedures in all four studies. The FMA-LE assessment consists of 17 items and is the LE motor sub-section of the FMA, with 2 items measuring reflex activity, 11 items measuring synergistic movements and 3 items measuring coordination (Table 1). Scoring of each item is based on a 3-point ordinal scale (0 = cannot perform, 1 = performs partially and 2 = performs fully), except two reflex items (Table 1).

TABLE 1.

The Lower Extremity section of the Fugl-Meyer Assessment Scale

Test	Item #	Item	Scoring Criteria
I. Reflex Activity	1	Achilles	0- No reflex activity can be elicited 2- Reflex activity can be elicited
	2	Patellar
II. Flexor Synergy (in supine)	3	Hip Flexion	0- Cannot be performed at all 1- Partial motion 2- Full motion
	4	Knee Flexion
	5	Ankle Dorsiflexion
III. Extensor Synergy (in side lying)	6	Hip Extension	0- Cannot be performed at all 1- Partial motion 2- Full motion
	7	Adduction
	8	Knee Extension
	9	Ankle Plantar Flexion
IV. Movement combining synergies (sitting: knees free of chair)	10	Knee Flexion beyond 90°	0- No active motion 1- From slightly extended position, knee can be flexed but not beyond 90° 2- Knee flexion beyond 90°
	11	Ankle Dorsiflexion	0- No active flexion 1- Incomplete active flexion 2- Normal Dorsiflexion
V. Movement out of synergy (Stnding hip at 0°)	12	Knee Flexion	0- Knee cannot flex without hip flexion 1- Knee begins flexion without hip flexion, but does not reach to 90° or hip flexes during motion 2- Full motion as described
	13	Ankle Dorsiflexion	0- No active motion 1- Partial motion 2- Full motion
VI. Normal Reflexes (sitting)	14	Knee flexors Patellar Achilles	0- At least 2 of 3 phasic reflexes are markedly hyperactive 1- One reflex is markedly hyperactive or at least 2 reflexes are lively 2- No more than one reflex is lively and none are hyperactive
VII. Coordination/Speed-Sitting: Heel to opposite knee (5 repetitions in rapid succession)	15	Tremor	0- Marked tremor 1- Slight tremor 2- No tremor
	16	Dysmetria	0- Pronounced or unsystematic dysmetria 2- No dysmetria
	17	Speed	0- Activity is more than 6 seconds longer than unaffected side 1- (2-5-9) seconds longer than unaffected side 2- Less than 2 seconds difference

Data Analysis

Data Management

Item 1 (‘Achilles reflex’) and item 2 (‘Patellar reflex’) are measured on a 2-point ordinal scale as opposed to the rest of the items measured on a 3-point scale. Therefore, these items were rescored by assigning scores of ‘2’ a score of ‘1’to be consistent with the rating of other items in the scale. The item ‘normal reflexes’ was deleted from all follow-up data analyses since it is not a dependent item and was scored based on the overall performances of other items. Sixteen items were used for confirmatory factor analysis (CFA) and a reduced set of 11 synergy items was used for principal components analysis (PCA) and Rasch analysis.

Psychometric Properties Analyses

Psychometric properties were analyzed in the following steps. First, a CFA (analyzed with Mplus 7.1),²² validated the hypothesized three-factor model. We chose weighted least squares means and variance adjusted (WLSMV) estimation as our model estimation method because the WLSMV is a robust estimator that does not assume normal distribution of variables, providing the best estimates when modelling categorical or ordered data.²³ The WLSMV provides model fit statistics such as comparative fit index (CFI), Tucker-Lewis index (TLI) and root mean square error of approximation (RMSEA) indices to identify the level of fit to the proposed model. We classified the items into three factors based on their descriptions: reflex (items 1–2), abnormal synergy (items 3–13) and coordination (items 15–17). The CFI, TLI and RMSEA indices explained the CFA results. The CFI/TLI compares the hypothesized model to a null model (with no factor at all); with benchmarks > 0.95 representing a good model fit, 0.90–0.95 representing a marginal model fit, and <0.90 representing a poor model fit.²⁴ The RMSEA compares expected values with actual values in a matrix after adjusting for sample size, a value less than 0.06 represents a good model fit.²⁴

We used the Rasch analysis rating scale model (RSM) to examine unidimensionality and item-difficulty hierarchy of the 11 abnormal synergy items. Rasch RSM was used because all the synergy items have the same 3-point rating scale structure. We also used Rasch residual PCA to examine unidimensionality of the scale. The PCA enables extraction of the primary (unidimensional) Rasch dimension enabling us to determine if the remaining residuals are meaningful or simply noise. The Rasch residual PCA can identify both the unidimensional Rasch dimension and the first contrast (that is, the first component in the correlation matrix of the residuals after extracting Rasch dimension).^25–27 Unidimensionality of a scale is suggested to be validated when the Rasch dimension explains 40% variance of the data, the first contrast of Rasch residual explains less than 5% variance of the data, and the eigenvalue of the first contrast is less than or equal to 2.0.^25–27 Both CFA and the Rasch residual PCA were used to determine whether the latent trait underlying the data is unidimensional.²⁸ However, we recognize that the Rasch residual PCA method has the limitation of identifying only patterns in the data since the purpose of the PCA residuals method is to explain variance (primary Rasch measurement component and the remaining residual component) instead of constructing factors of the scale.

Following factor structure analysis (CFA and the Rasch residual PCA), we performed Rasch analysis to examine unidimensionality of the scale. In contrast to classical test theory, Rasch analysis is an item-level analysis where the ability level of the person and the difficulty level of the items are placed on the same continuous variable providing statistics at the item and person level. Winsteps 3.75²⁹ was used to examine the item-level psychometric properties of the scale, including rating scale diagnosis statistics, person and item fit statistics, point-measure correlation, person separation reliability, person separation strata and ceiling/floor effects. The three main criteria for examining a rating scale included; a minimum of ten responses in each rating category, a monotonic pattern of category measure, and the outfit mean square for each rating scale category less than 2.0.³⁰ While the point-measure correlation is the Pearson correlation between the observations and the Rasch measures accounting for all observations, the expected point-measure correlation is the one between the expected observations and the Rasch measures. The person and item fit statistics were determined by the Infit mean square (Infit MNSQ) and Outfit mean square (Outfit MNSQ) value with a range of 0.6 to 1.4 and the value of standardized fit statistics (ZSTD) within ±2.³¹ The infit and outfit MNSQ values (fit statistics) are chi-square ratios that examine how well the empirical data fit the requirements of the ideal model.²⁸ Infit is an information-weighted fit statistics weighted by model variance, whereas outfit is an outlier-sensitive fit statistics.³² Person separation reliability, analogous to Cronbach’s alpha, indicates the levels of person reliability across all items^33,34 with the value of α ≥ 0.90 suggested for clinical application.³⁵ In addition, we calculated person strata using person separation index. Person separation index (Gp) is defined as true standard deviation (i.e., observed standard deviation² − average measurement error²) divided by averaged measurement error.³⁶ Person strata, calculated as (4Gp + 1)/3,³⁷ is the number of ability level with the center value three measurement errors apart, representing the level of person ability distinguished by all items. From a measurement perspective, instruments should be able to statistically divide a sample into at least three distinct person strata.³³ The ceiling/floor effects were determined by the item-person map,³⁸ using a standardized logit unit to place item-difficulty and person ability in the same continuum.

RESULTS

Pooled data from the four studies resulted in a total number of 535 individuals with stroke. The participant characteristics available from each study and of the pooled sample are summarized in the on-line only appendix.

3-factor Model Fit

The CFI/TLI values for the 3-factor model were 0.95/0.94, respectively. Whereas, the RMSEA value was 0.124. The reflex items showed high error variance (Patellar = 2584.41, Achilles = 176.84); followed by the coordination items (Tremor = 2.91; Dysmetria = 1.49; Speed = 9.41). The error variance for the 11 abnormal synergy items were low (0.06 – 0.31). Additionally, the reflex construct had only 2 items and the coordination construct had only 3 items; therefore, the remainder of the analyses focused on the measurement properties of the synergy construct (11 items).

Dimensionality, Item-difficulty hierarchy and Item-fit statistics of the 11 abnormal synergy items

The Rasch dimension of the 11 abnormal synergy items explained a total 90.8% of the variance in the data and no meaningful residuals were left after extracting this Rasch dimension. Additionally, the rating scale diagnostics met all three essential rating scale criteria. Point-measure correlations were also acceptable and the infit statistics for the 11 items fell within the guidelines (Table 2). However, 3 items had high outfit values, including item 7 ‘Within synergy – hip adduction’ (Outfit MNSQ=2.28, ZSTD=4.6), item 3 ‘Within synergy – hip flexion’ (Outfit MNSQ=1.92, ZSTD=2.8), and item 6 ‘Within synergy – hip extension’ (Outfit MNSQ=1.90, ZSTD=2.7), Table 2. The difficulty level of the items ranged from −2.24 to 3.27 logits (5.51 logit range). Item 12 ‘out of synergy – knee flexion’ (3.27 ± 0.09 logits) and item 13 ‘out of synergy – ankle dorsiflexion’ (3.05 ± 0.09 logits) were the most difficult items. Conversely, item 8 ‘within synergy – knee extension’ (−2.24 ± 0.14 logits) and item 6 ‘within synergy – hip extension’ (−1.63 ± 0.12 logits) were the easiest items.

TABLE 2.

Item Measure Table of the 11Abnormal Synergy Items

Item No.	Item Name	Score			Infit		Outfit		Pt. Measure Correlation
		Raw	Mean Measure	Model S.E.	MNSQ	ZSTD	MNSQ	ZSTD	Observed	Expected
12	Out of synergy – knee flexion	301	3.27	0.09	0.97	−0.4	0.93	−0.4	0.77	0.77
13	Out of synergy – ankle dorsiflexion	326	3.05	0.09	0.76	−3.9	0.68	−2.4	0.82	0.78
11	Combined synergy – ankle dorsiflexion	529	1.36	0.09	0.8	−3.4	0.7	−3.7	0.82	0.78
5	Within synergy – ankle dorsiflexion	631	0.48	0.10	0.86	−2.1	0.71	−3.1	0.79	0.76
9	Within synergy – ankle plantarflexion	673	0.08	0.10	1.29	3.9	1.29	2.2	0.71	0.74
10	Combined synergy – knee flexion	721	−0.41	0.10	0.85	−2.1	0.67	−2.4	0.75	0.72
7	Within synergy – hip adduction	777	1.05	0.11	1.3	3.5	2.28	4.6	0.61	0.68
4	Within synergy – knee flexion	803	−1.4	0.12	0.85	−1.8	0.61	−1.7	0.7	0.66
3	Within synergy – hip flexion	812	−1.52	0.12	0.93	−0.8	1.92	2.8	0.65	0.66
6	Within synergy – hip extension	819	−1.63	0.12	1.16	1.8	1.9	2.7	0.6	0.65
8	Within synergy – knee extension	856	−2.24	0.14	1.04	0.4	1.5	1.3	0.58	0.61

The person ability ranged from −4.54 to 5.01, with a 9.55 logit range (Figure 1). Person ability was one standardized deviation higher than item-difficulty. The mean person ability was 1.73 logits higher than the mean item-difficulty. Ten percent of the sample (51/535=9.5%) had the maximum raw score (highest ability), indicating a ceiling effect (Figure 1). Additionally, the person separation reliability index was 0.91, person separation index was 2.37 and person separation strata were 3.49 for the 11 abnormal synergy items.

Figure 1. Item person map of the 11 abnormal synergy items.

This figure presents a map of person abilities and the 11 abnormal synergy item difficulties plotted on a logit scale. Person abilities (“..”- representing 1–4 persons, “#” representing 5 persons) range from a low of −5 logits at the bottom of the figure to a high of 6 logits at the top of the figure. Items are plotted at their mean difficulty level with items that are easier to endorse at the bottom of the map and items that are difficult to endorse at the top of the map. Letters to the left of the vertical dashed line are means and standard deviations for person abilities and to the right of the vertical line are mean and standard deviations for the item difficulties. Abbreviations: M = mean, S = 1 standard deviation and T = 2 standard deviations.

DISCUSSION

The purpose of this study was to investigate the dimensionality and item-difficulty hierarchy of the FMA-LE. Application of IRT-based methodologies supported our hypothesis that FMA-LE represents a multidimensional construct, reflecting three distinct constructs: reflex, abnormal synergy and coordination. After removing the reflex and coordination items, the 11 abnormal synergy items of the FMA-LE scale contributed to the measurement of a single construct. However, the difficulty order of the abnormal synergy items deviated from the stepwise recovery process proposed by others. Our findings have implications for using the total score of the FMA-LE assessment to predict lower extremity motor recovery.

Results from the CFA and Rasch PCA supported our hypothesis of multidimensionality. First, the CFA showed adequate to good fit of a 3-factor model with 2/3 indices showing good model fit. Specifically, the CFI/TLI values of 0.95/0.94 showed good model fit whereas the RMSEA value of 0.124 (>0.06) did not meet the model fit criteria. Second, the Rasch PCA revealed that after removal of the reflex and coordination factors, the abnormal synergy factor explained a substantial (90.8%) variance in the data, implying that the reflex and coordination items measure a different construct when compared to the abnormal synergy items. Therefore, based on our findings of multidimensionality, we suggest discontinuing the use of the total score (34) of the FMA-LE to measure motor recovery. However, our findings of multidimensionality should be considered preliminary since not all the model fit criteria were met for the hypothesized 3-factor model. Future studies are warranted to confirm our findings.

Multidimensionality of the FMA is also implicitly suggested in other reports.^16,39 When evaluating the measurement characteristics of the upper extremity section of the FMA, Woodbury and colleagues showed that the upper extremity reflex items misfit the construct measured by the rest of the items suggesting a multidimensional assessment.³⁹ Involuntary reflexive behaviors are also physiologically different from voluntary movements (such as those movements occurring within, combining and out of synergies).¹⁴ While developing a short form of the FMA, Hsieh and colleagues reported that not only the reflex items but 2/3 of the coordination items (‘Tremor’ and ‘Dysmetria’) had high fit statistics and subsequently removed them from the short form.¹⁶ Notably, coordination as captured by the FMA-LE is also considerably different from the intra- and inter-limb coordination required for lower extremity functions, such as walking.^40–42 Therefore, the multidimensionality of FMA-LE has some literature support.

While our results suggested that the FMA-LE was multidimensional, the 11 abnormal synergy items seemed unidimensional. However, the item-difficulty hierarchy of the unidimensional abnormal synergy items revealed several deviations from the originally proposed stepwise sequence of motor recovery.¹² For instance, Item 12 ‘Out of synergy – knee flexion’ was calibrated as the most challenging item contrary to the original hierarchy. This item requires flexing the affected knee in standing and its high difficulty level can be explained by the additional balance demands to support weight on one leg. Another deviation from the original hierarchy was that of the ankle items. All ankle items irrespective of whether movement occurred within, combining or outside of synergies clustered towards the more difficult end of the hierarchy. Contemporary motor control literature provides some rationale for why the ankle items, irrespective of the synergy pattern, maybe more challenging than the proximal hip and knee movements. Ankle dorsiflexor and plantarflexor muscle groups receive direct corticospinal innervation during voluntary activities.⁴³ Therefore, damage to the corticospinal tract may be expected to cause greater impairment in ankle control compared to proximal hip and knee joints. Our finding of distal ankle control being harder than proximal hip and knee control also conflicts with the proximal-to-distal sequence suggested in the earlier motor recovery works.⁴⁴

In addition to the deviations in item-difficulty hierarchy of the abnormal synergy items, several of these items were calibrated at similar difficulty levels suggesting measurement redundancy. Additionally, the abnormal synergy items revealed moderate internal consistency, had substantial ceiling effect and the discriminatory ability seemed low (person separation index = 2.36). Therefore, while the abnormal synergy items were unidimensional, measurement could be improved by revising current items along with potentially addition of new items. Nonetheless, it is notable that the investigation of the staged hierarchical progression in the FMA-LE is inherently limited by the structure and the procedures of the assessment. There are an unequal number of items across the progressive stages (i.e. only 2 items each represent the combined and out-of-synergy movements whereas 7 items represent the within synergy movements). Moreover, the postural transitions from supine to sitting and ultimately to standing that are required for assessing the successive stages of motor recovery additionally create balance demands. Nevertheless, until an improved version is developed, the abnormal synergy score may remain of value for assessing LE motor control. Therefore, we suggest discontinuing the use of the total score of the FMA-LE and use the abnormal synergy score to predict lower extremity motor recovery.^19,40,45

Our suggestions are different from others. Crow and colleagues investigated the hierarchical properties of the motor sections of both upper and lower extremity FMA in individuals with acute and chronic stroke and supported the use of a total score of the FMA.^46,47 The inconsistent results may primarily be due to different study methodologies Crow and colleagues used the Guttman scale analysis as opposed to CFA and Rasch analysis.^46,47 They propose that the Guttman scale analysis is suitable to investigate the hierarchical properties of the FMA due to the underlying nature of the construct, i.e. staged progression of motor recovery. However, Crow et al^46,47 do not take into account the concept of a linear continuum (which they refute) and staged progressions (which they support) are separate. Linearity reflects whether all items measure a linear construct whereas staged progression refers to where individuals lie on that linear construct.

Despite the differences in methodology between our study and Crow et al.’s work,^46,47 there are many similarities in our results. Item 12 ‘out of synergy - knee flexion’ was the most challenging item in both our and Crow et al.’s study. Furthermore, similar to our findings, Crow et al. reported that the ankle items were the next most challenging items clustering towards the harder end of the hierarchy. Lastly, both our findings and Crow et al.’s study found that the within-synergy hip and knee items were the least challenging. Individual hip and knee items deviated from their strict ordering within-synergy in both studies. Only the ordering of one item (Item 10 ‘combined synergy – knee flexion’) differed between our results. In our results Item 10 was one of the easier items, whereas in Crow et al.’s study it was one of the more challenging items. Despite their findings of deviations in the rank ordering similar to our results, Crow et al. suggest the continued use of a total score. Contrarily, our findings of misfit items conflict with the use a total score of the FMA-LE.

Study limitations

Note that, since this is a retrospective study, the generalizability of the study is limited. Additionally, several assessors were involved in the four studies which could attribute to instrumentation error. We also recognized that our proposed 3-factor model included two factors (i.e. reflex and coordination) with low number of items (i.e. two items for reflex factor and three items for coordination factor). Thus, the items for these two factors may not be able to completely capture the latent trait of each.

CONCLUSIONS

Our results are suggestive of multidimensionality of the FMA-LE, conflicting the use of a total FMA-LE score to measure motor recovery. Particularly, use of a total score from a multidimensional assessment may decrease the construct validity of the FMA-LE, contributing to lower responsiveness of the scale to interventions aimed at improving lower extremity motor recovery. Removal of the misfit items of reflex and coordination resulted in 11 items (assessing abnormal synergy) that contribute to the measurement of a single construct. While these 11 abnormal synergy items were unidimensional, the hierarchical ordering of item-difficulty deviated from the ‘stepwise’ sequence of motor recovery originally proposed by the instrument developers suggesting improvement in these items. In the interim, the abnormal synergy score may prove to be useful to measure lower-extremity motor recovery.

• The lower-extremity fugl-meyer assessment represents a multi-dimensional construct.

• Our results challenge use of the total score to predict lower-extremity motor recovery.

• The abnormal synergy items of the lower-extremity fugl-meyer are unidimensional.

• The abnormal synergy items deviate from the originally proposed hierarchical order.

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Abbreviations

FMA-LE

Fugl-Meyer assessment of lower extremity

IRT

Item-response theory

CFA

Confirmatory factor analysis

PCA

Principal component analysis

CFI

Comparative fit index

TLI

Tucker-Lewis index

RMSEA

Root mean square error of approximation

RSM

Rating scale model

MNSQ

Mean square error

ZSTD

Standardized fit statistics

Gp

Person separation index