An examination of the structural validity of the Physical Self-Description Questionnaire-Short Form (PSDQ–S) using the Rasch Measurement Model

Figures & data

Table 1. Physical Self-Description Questionnaire-Short Form (PSDQ–S) subscale descriptive statistics (N = 117)

	PA	AP	BF	CO	EN	SE	FL	GP	HE	SP	ST	Total Scale Score
Mean	19.11	12.28	11.41	24.58	13.99	22.63	12.72	15.60	18.32	15.16	14.17	179.98
Std. Deviation	4.40	3.18	6.25	4.44	3.37	4.87	3.80	2.55	8.58	3.15	3.14	27.07
Range	15	15	15	16	12	20	15	11	25	15	12	129
25th Percentile	16	10	3	22	12	18	10	14	10	13	12	164
50th Percentile	20	12	13	26	14	22	13	16	19	16	15	177
75th Percentile	23	15	18	28	17	27	15	18	27	18	17	198

PA = Activity; AP = Appearance; BF = Body Fat; CO = Coordination; EN = Endurance; SE = Global Esteem;

FL = Flexibility; GP = General Physical; HE = Health; SP = Sport; ST = Strength

Table 2. Total Physical Self-Description Questionnaire-Short Form (PSDQ–S) Rasch Measurement Model (RMM) composite item statistics (N = 117)

PSDQ–S Scale Items	RMM Logit Item Measure	Logit Item Measure S. E.	Infit MNSQ	Infit ZSTD	Outfit MNSQ	Outfit ZSTD	Point Measure Correlation
PSDQ–S 34	.88	.07	1.37	2.6	1.24	1.5	.56
PSDQ–S 31*	.75	.07	1.49	3.7	1.41	2.7	.52
PSDQ–S 32	.73	.07	1.33	2.6	1.25	1.7	.54
PSDQ–S 20	.73	.07	1.30	2.4	1.23	1.6	.55
PSDQ–S 10	.68	.06	1.42	3.3	1.33	2.2	.53
PSDQ–S 23	.67	.06	1.32	2.6	1.27	1.9	.51
PSDQ–S 8	.66	.06	1.33	2.7	1.27	1.9	.52
PSDQ–S 33	.62	.06	.98	−.1	.96	−.3	.49
PSDQ–S 9	.60	.06	1.38	3.2	1.33	2.4	.48
PSDQ–S 6	.51	.06	.79	−2.1	1.30	2.2	.39
PSDQ–S 30	.49	.06	1.12	1.1	1.32	2.3	.36
PSDQ–S 26	.11	.07	.80	−1.9	.99	.0	.37
PSDQ–S 25	.10	.07	1.06	.5	1.74	4.2	.26
PSDQ–S 7	−.02	.07	.74	−2.3	.83	−1.1	.37
PSDQ–S 5	−.02	.07	.89	−.9	1.48	2.7	.27
PSDQ–S 1	−.03	.07	.99	.0	1.19	1.2	.35
PSDQ–S 17	−.03	.07	.81	−1.6	.89	−.7	.41
PSDQ–S 24	−.03	.07	.82	−1.5	1.08	.6	.36
PSDQ–S 40	−.06	.07	.85	−1.2	.95	−.2	.35
PSDQ–S 16	−.10	.07	.84	−1.2	1.07	.4	.36
PSDQ–S 38	−.14	.07	.79	−1.7	.93	−.4	.32
PSDQ–S 4	−.19	.07	1.01	.1	1.11	.7	.37
PSDQ–S 19	−.20	.07	.64	−2.9	.67	−2.0	.37
PSDQ–S 14	−.26	.08	.62	−2.9	.68	−1.9	.42
PSDQ–S 13	−.29	.08	.70	−2.2	.73	−1.5	.40
PSDQ–S 18	−.29	.08	.73	−1.9	.89	−.6	.37
PSDQ–S 15	−.29	.08	.78	−1.5	.74	−1.5	.38
PSDQ–S 3	−.30	.08	1.22	1.4	1.22	1.2	.35
PSDQ–S 35	−.31	.08	.89	−.7	1.04	.3	.36
PSDQ–S 39	−.33	.08	.86	−.9	1.05	.3	.37
PSDQ–S 11	−.34	.08	.70	−2.1	.77	−1.2	.37
PSDQ–S 12	−.35	.08	1.00	.1	1.11	.6	.30
PSDQ–S 36	−.36	.08	.86	−.9	1.09	.5	.35
PSDQ–S 2	−.38	.08	1.16	1.0	1.33	1.6	.32
PSDQ–S 21	−.42	.08	.64	−2.4	.70	−1.6	.36
PSDQ–S 27	−.45	.09	.93	−.4	.93	−.3	.33
PSDQ–S 28	−.53	.09	.78	−1.3	.89	−.5	.33
PSDQ–S 37	−.53	.09	.67	−2.0	.63	−1.9	.41
PSDQ–S 29	−.59	.09	.85	−.8	1.02	.2	.30
PSDQ–S 22	−.73	.10	.77	−1.1	.80	−.8	.30

* misfitting item according to RMM requirements of MNSQ range between 0.60–1.4, ZSDT range between −2 and 2, and/or Point Measure Correlation <0.20

Note: RMM = Rasch Measurement Model; PSDQ–S = Physical Self-Description Questionnaire-Short Form; MNSQ = Mean Square; ZSTD = z-standardized

Table 3. Physical Self-Description Questionnaire-Short Form (PSDQ–S) Rasch Measurement Model (RMM) subscale item statistics (N = 117)

PSDQ–S Scale Items	RMM Logit Item Measure	Logit Item Measure S. E.	Infit MNSQ	Infit ZSTD	Outfit MNSQ	Outfit ZSTD	Point Measure Correlation
Activity (PA)
PSDQ–S 1	.35	.09	1.40	3.2	1.32	1.9	.70
PSDQ–S 4	.06	.10	.62	−2.8	.63	−2.5	.76
PSDQ–S 3	−.14	.10	.89	−.7	.82	−1.1	.70
PSDQ–S 2	−.28	.10	1.21	1.3	1.13	.8	.63
Appearance (AP)
PSDQ–S 6	1.41	.13	1.21	1.5	1.23	1.6	.79
PSDQ–S 7	−.70	.13	.73	−2.2	.70	−2.3	.85
PSDQ–S 5	−.71	.13	1.06	.5	1.01	.1	.81
Body Fat (BF)
PSDQ–S 8	.12	.16	.95	−.2	.88	−.5	.86
PSDQ–S 9	−.06	.16	1.1	.1	1.01	.1	.85
PSDQ–S 10	−.06	.16	.98	0	.92	−.3	.33
Coordination (CO)
PSDQ–S 14	.11	.12	.84	−1.0	.86	−.9	.72
PSDQ–S 13	.04	.12	.80	−1.4	.88	−.8	.74
PSDQ–S 15	.03	.12	.71	−2.1	.63	−2.7	.77
PSDQ–S 11	−.07	.12	1.22	1.4	1.28	1.7	.62
PSDQ–S 12	−.10	.12	1.41	2.4	1.38	2.2	.65
Endurance (EN)
PSDQ–S 17	.35	.12	.94	−.3	.93	−.5	.84
PSDQ–S 16	.11	.13	1.06	.4	1.01	.1	.81
PSDQ–S 18	−.46	.13	.95	−.3	.95	−.3	.78
Global Esteem (SE)
PSDQ–S 20	.89	.08	.69	−2.3	.63	−2.4	.80
PSDQ–S 23	.81	.08	.95	−.3	.99	.0	.75
PSDQ–S 19	−.25	.08	.68	−2.3	1.21	1.2	.44
PSDQ–S 21	−.52	.09	.68	−1.8	1.03	.2	.42
PSDQ–S 22	−.93	.12	1.19	.9	1.30	1.3	.31
Flexibility (FL)
PSDQ–S 26	.19	.13	1.01	.1	.99	.0	.85
PSDQ–S 25	.16	.13	.98	−.1	.90	−.7	.86
PSDQ–S 24	−.34	.13	.98	−.1	.97	−.2	.84
General Physical (GP)
PSDQ–S 27	.19	.14	1.06	.4	1.03	.3	.78
PSDQ–S 28	−.02	.15	.91	−.4	.95	−.2	.78
PSDQ–S 29	−.17	.15	.98	.0	1.04	.3	.77
Health (HE)
PSDQ–S 34	.41	.10	1.03	.2	.75	−1.2	.83
PSDQ–S 31	.11	.10	1.09	.6	.81	−1.0	.82
PSDQ–S 32	.08	.10	.71	−1.9	.56	−2.6	.86
PSDQ–S 33	−.17	.09	.88	−.8	.91	−.4	.85
PSDQ–S 30	−.44	.09	1.33	2.1	1.83	3.7	.76
Sport (SP)
PSDQ–S 35	.43	.17	.85	−.8	.85	−.9	.90
PSDQ–S 36	.15	.18	1.09	.5	1.08	.5	.86
PSDQ–S 37	−.58	.19	.96	−.2	.83	−1.0	.86
Strength (ST)
PSDQ–S 40	.37	.13	1.04	.3	1.01	.1	.83
PSDQ–S 38	.12	.13	.78	−1.6	.80	−1.4	.84
PSDQ–S 39	−.49	.14	1.24	1.5	1.10	.7	.77

* misfitting item according to RMM requirements of MNSQ range between 0.60–1.4 and ZSDT range between −2 and 2

Note: RMM = Rasch Measurement Model; PSDQ–S = Physical Self-Description Questionnaire-Short Form; MNSQ = Mean Square; ZSTD = z-standardized; PA = Activity; AP = Appearance; BF = Body Fat; CO = Coordination; EN = Endurance; GE = Global Esteem; FL = Flexibility; GP = General Physical; HE = Health; SP = Sport; ST = Strength

Table 4. Parameters of the Physical Self-Description Questionnaire-Short Form (PSDQ–S) composite and subscales with Rasch Measurement Model (RMM) requirements (N = 117)

Parameter	RMM requirements	PSDQ–S total scale (40 items)	PSDQ–S Activity subscale (4 items)	PSDQ–S Appearance subscale (3 items)	PSDQ–S Body Fat subscale (3 items)	PSDQ–S Coordination subscale (5 items)	PSDQ–S Endurance subscale (3 items)
Model Requirements
Monotonicity	Visual inspection of item thresholds; all thresholds order	✓	✓	✓	✓	✓	✓
Local Independence	r >0.3 between the standardized residuals of the Rasch analysis between any item pairs would violate local independence	✓	✓	✓	✓	✓	✓
Unidimensionality	PCA analysis of item residuals	✓	✓	✓	✓	✓	✓
Differential Item Functioning	Percentage of items demonstrating DIF is <5%	× one item exhibited DIF	✓	✓	✓	✓	✓
Model Fit: summary of items
Item hierarchy: face validity	Item hierarchical ordering conforms to theoretical/clinical expectations	✓	✓	✓	✓	✓	✓
Item mean (SD) logits	0.0	0.00 (0.45)	0.00 (0.24)	0.00	0.00 (0.08)	0.00 (0.08)	0.0 (0.34)
Item reliability*	>0.8	0.97 [excellent]	0.80 [fair]	0.98 [excellent]	0.95 [excellent]	0.94 [very good]	0.86 [very good]
Item separation index	>3.0	5.71	1.98	7.34	1.28	1.25	2.44
Item spread		1.61	0.60	2.12	0.18	0.21	0.81
Item Model Init MNSQ Range Extremes*	0.60–1.4	0.62–1.49 [fair]	0.62–1.40 [very good]	0.73–1.21 [very good]	0.95–1.01 [fair]	.71–1.41 [very good]	0.94–1.06 [fair]
Item Model Infit ZSTD Range Extremes	−2.0–+2.0	(−2.9) to 3.7	(−2.8) to 2.5	(−2.2) to 1.5	(−3.8) to 2.9	(−2.1) to 2.4	(−0.3) to 0.5
Item Model Outfit MNSQ Range Extremes*	0.60–1.4	0.63–1.74 [fair]	0.63–1.32 [good]	0.7–1.23 [very good]	0.5–2.42 [good]	0.63–1.38 [good]	0.93–1.01 [fair]
Item Model Outfit ZSTD Range Extremes	−2.0–+2.0	(2.0) to 4.2	(−2.5) to 1.9	(−2.3) to 16	(−3.6) to 6.4	(−2.7) to 2.2	(−0.5) to 0.1
# misfitting items	0	1 (2.5%)	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)
PSDQ–S misfitting items		31	NA	NA	NA	NA	NA
# Separate Item Strata*	>3	8.0 [good]	3.0 [fair]	10.1 [excellent]	2.0 [poor]	2.0 [poor]	3.6 [good]
Model Fit: summary of persons
Person spread		3.82	3.22	7.69	6.42	4.2	5.34
Person mean (SD) logits		0.46 (0.60)	0.74 (0.85)	0.94 (1.75)	0.51 (1.79)	1.47 (1.20)	1.04 (1.39)
# misfitting persons	<5%	1 (0.85%)	28 (23.9%)	6 (5.1%)	69 (59%)	14 (12%)	26 (22.2%)
Measurement quality: reliability and targeting
Person reliability*	>0.80 for individual measurement	0.90 [very good]	0.51 [poor]	0.71 [fair]	0.78 [fair]	0.64 [poor]	0.62 [poor]
Person Separation Index (PSI)	>2.0	3.05	1.03	1.56	1.86	1.35	1.27
# of Separate Person Strata*	>3 strata for individual measurement	4.4 [very good]	1.7 [poor]	2.4 [fair]	2.8 [fair]	2.1 [fair]	2.0 [fair]
Person Raw Score Reliability	>0.80 for individual measurement	0.91	0.75	0.77	0.96	0.81	0.79
Standard Error of Measurement (SEM)	Standard Error of Measurement (SEM) as low as possible	0.20	0.60	0.94	0.84	0.72	0.86
Precision of the person measure estimates	Expected to be higher in the middle of the measurement range	25	2.78	1.17	1.43	1.93	1.35
Targeting—Targeting Index*	When average person measure is [−1, 1] targeting is good; when [−2, 2] targeting is fair	0.46: 25 [fair]	0.74: 0.60 [good]	0.94: 1.17 [good]	0.51: 0.84 [fair]	1.47: 0.72 [poor]	1.04: 0.86 [fair]
Ceiling effect (% of persons with maximum score)*	<2–5%	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]
Floor effect (% of persons with minimum score)*	<2–5%	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]
Difference between person & item means	<1.0 logit	0.46	0.74	0.94	0.51	1.47	1.04
Dimensionality
Variance accounted for by 1st factor*	>60%	69.2% [good]	61.5% [good]	78.7% [very good]	84.1% [excellent]	60.1% [good]	67.9%[good]
PCA (eigenvalue for 1st contrast)	≤2.0	9.6	1.6	1.7	1.6	1.6	1.6
Unexplained variance in contrasts 1–5 of PCA of residuals*	<5%	1.4% [excellent]	0.0% [excellent]	0.0% [excellent]	0.0% [excellent]	0.0% [excellent]	0.0% [excellent]
Differential Item Functioning
DIF by gender (total # of items [% of total number of items])	>0.5 logits; p < .05	1 (2.5%)	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)
Item # exhibiting DIF by gender		25	NA	NA	NA	NA	NA
Model Requirements
Monotonicity	Visual inspection of item thresholds; all thresholds order	✓	✓	✓	✓	✓	✓
Local Independence	r >0.3 between the standardized residuals of the Rasch analysis between any item pairs would violate local independence	✓	✓	✓	✓	✓	✓
Unidimensionality	PCA analysis of item residuals	✓	✓	✓	✓	✓	✓
Differential Item Functioning	Percentage of items demonstrating DIF is <5%	✓	✓	× one item exhibited DIF	✓	✓	✓
Model Fit: summary of items
Item hierarchy: face validity	Item hierarchical ordering conforms to theoretical/clinical expectations	✓	✓	✓	✓	✓	✓
Item mean (SD) logits	0.0	0.0 (0.73)	0.0 (0.24)	0.0 (0.15)	0.0 (0.29)	0.0 (0.43)	0.0 (0.36)
Item reliability*	>0.8	0.98 [excellent]	0.71 [fair]	0.61[poor]	0.88 [good]	0.82 [good]	0.85 [good]
Item separation index	>3.0	7.58	1.57	1.08	2.67	2.11	2.37
Item spread		1.82	0.53	.32	0.85	1.01	0.86
Item Model Infit MNSQ Range Extremes*	0.60–1.4	0.68–1.19 [fair]	0.98–1.01 [fair]	0.91–1.06 [fair]	0.71–1.33 [very good]	0.85–1.09 [fair]	0.78–1.24 [very good]
Item Model Infit ZSTD Range Extremes	−2.0–+2.0	−2.3–0.9	−0.1–0.1	−0.4–0.4	−1.9–2.1	−0.8–0.5	−1.6–1.5
Item Model Outfit MNSQ Range Extremes*	0.60–1.4	0.63–1.30 [good]	0.90–0.99 [poor]	0.95–1.04 [poor]	0.56–1.83 [poor]	0.83–1.08 [poor]	0.80–1.10 [poor]
Item Model Outfit ZSTD Range Extremes	−2.0–+2.0	−2.4–1.3	−0.7 to 0.6	−0.20–0.3	−2.6–3.7	−1.0–0.50	−1.4–0.7
# misfitting items	0	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)
PSDQ–S misfitting items		NA	NA	NA	NA	NA	NA
# Separate Item Strata*	>3	10.4 [excellent]	2.4 [fair]	1.8 [poor]	3.9 [good]	3.2 [good]	3.5 [good]
Model Fit: summary of persons
Person spread		3.81	7.76	4.66	4.87	7.12	5.69
Person mean (SD) logits		0.41 (0.80)	0.76 (1.76)	1.35 (1.37)	0.45 (1.32)	1.73 (2.00)	1.18 (1.47)
# misfitting persons	<5%	10 (8.5%)	18 (15%)	41 (35%)	11 (9.4%)	45 (38.5%)	25 (21.4%)
Measurement quality: reliability and targeting
Person reliability*	>0.80 for individual measurement	0.57 [poor]	0.73 [fair]	0.47 [fair]	0.77 [fair]	0.69 [fair]	0.62 [poor]
Person Separation Index (PSI)	>2.0	1.16	1.63	0.95	1.85	1.48	1.28
# of Separate Person Strata*	>3 strata for individual measurement	1.9 [poor]	2.5 [fair]	1.6 [poor]	2.8 [fair]	3.9 [good]	2.0 [fair]
Person Raw Score Reliability	>0.80 for individual measurement	0.60	0.84	0.72	0.91	0.88	0.78
Standard Error of Measurement (SEM)	Standard Error of Measurement (SEM) as low as possible	0.34	0.91	0.90	0.63	1.11	0.91
Precision of the person measure estimates	Expected to be higher in the middle of the measurement range	8.65	1.21	1.23	2.73	0.81	1.21
Targeting—Targeting* Index	When average person measure is [−1, 1] targeting is good; when [−2, 2] targeting is fair	0.41: 0.34 [good]	0.76: 0.91 [fair]	1.36: 0.90 [poor]	0.45: 0.63 [fair]	1.73: 1.11 [poor]	1.18: 1.21 [good]
Ceiling effect (% of persons with maximum score)*	<2–5%	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]
Floor effect (% of persons with minimum score)*	<2–5%	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]	0% [excellent]
Difference between person & item means	<1.0 logit	0.41	0.76	1.35	0.45	1.73	1.18
Dimensionality
Variance accounted for by 1st factor*	>60%	65.9% [good]	76% [very good]	52.1% [poor]	87.8% [excellent]	66.9% [good]	64.2% [poor]
PCA (eigenvalue for 1st contrast)	≤2.0	1.4	1.6	1.6	2.3	1.7	1.6
Unexplained variance in contrasts 1–5 of PCA of residuals*	<5%	0% [excellent]	0% [excellent]	0% [excellent]	0.1% [excellent]	0% [excellent]	0% [excellent]
Differential Item Functioning
DIF by gender (total # of items [% of total # of items])	>0.5 logits; p < .05	0 (0.0%)	0 (0.0%)	1 (33.3%)	0 (0.0%)	0 (0.0%)	0 (0.0%)
Item number exhibiting DIF by gender		NA	NA	29	NA	NA	NA

RMM = Rasch Measurement Model; # = number; SD = Standard Deviation; PCA = Principal Components Analysis; DIF = Differential Item Functioning; MNSQ = Mean Square. NA = not applicable. Person spread is defined as the difference between maximum person logit score and minimum person logit score. Item spread is defined as the difference between maximum item logit score and minimum item logit score. ✓ denotes that the RMM quality assessment guideline requirement has been met, whereas × infers that the quality assessment guideline requirement has not been met.

* refers to Rating Scale Instrument Quality Criteria categories of “poor, fair, good, very good and excellent” developed by Fisher (2007). Citation: Fisher (2007). Rating scale instrument quality criteria. Rasch Measurement Transactions 21, 1095. Available from: http://www.rasch.org/rmt/rmt211.pdf

Figure 1. Wright person-item Rasch map for the PSDQ–S cpmposite scale (N = 117).

Figure 2. Wright person-item Rasch map for the PSDQ–2 subscales (N = 117).

Fisher, W. P., Jr. (2007). Rating scale instrument quality criteria. Rasch Measurement Transactions, 21, 1095. Retrieved from http://www.rasch.org/rmt/rmt211.pdf

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