Disordered gambling, or dependence and consequences: a bifactor exploratory structural equation model analysis of the problem gambling severity index

Figures & data

Table 1. Previous factor analyses of PGSI data.

Study	n	Sampling	Analytic Approach	Findings
EFA
Ferris and Wynne (2001)	3120	General population survey of Canadian adults	ML FA (factor retention not specified)	Iterative process – first set of analyses supported 3 F, divided heuristically into problems and consequences. However, analyses showed substantial cross-loading that made interpretation of factors unfeasible. Subsequent analysis with a reduced set of 20 items, then a final 9 item PGSI supported 1 F. Confirmatory analysis using parallel analysis.
Brooker et al. (2009)	742	Subset of Canadian general population survey (CCHS) with severe gambling and comorbidities	PCA (retention determined by the presence of significant loadings)	1 F structure supported, loadings = .52–.78.
Holtgraves (2008)	12299	Integrated dataset of multiple Canadian provinces.	PCA (Kaiser)	1 F structure supported across the sample (loadings = .634–.792), but factor structure is inconsistent across PGSI groupings.
So et al. (2019)	3586	Japanese general population survey	ML FA (MAP)	1 F structure supported, loadings = .31–.84.
Orford et al. (2010)	5483	British general population survey	PCA (Kaiser and factor loadings)	1 F supported, factor loadings = .61–.88.
James et al. (2014)	49	Subsample of British problem gamblers (PGSI 8+)	GLS FA (Kaiser)	2 F supported in subsample, F1 loadings = .595–.801, F2 loadings = .545–.950.
Bertossa et al. (2014)	299	Sample of indigenous Australian gamblers	PCA (Kaiser)	1 F structure supported, loadings not reported.
Arthur et al. (2008)	148	Singaporean student sample	ML FA (% variance explained > 50% on F1)	1 F structure supported on 12-item CPGI – loadings = .28–.88.
McMillen and Wenzel (2006)	141	Subsample of Australian general population survey – weekly gamblers	PCA (size of eigenvalue and % variance explained)	1 F structure supported, loadings > .69.
Currie et al. (2010)	12792	Split half of a mixture of Canadian general population surveys	PCA (eigenvalue and % of variance explained)	1 F structure supported with PCA, loadings = .599–.786. EFA analysis was conducted on ordinal PGSI data and then dichotomized items with a tetrachoric correlation matrix.
Barbaranelli et al. (2013)	1979	Representative Italian panel study	WLS FA (Kaiser, PA)	PA & eigenvalues converged on 1 F structure, loadings = .753–.904.
Molander and Wennberg (2022)	598	Four populations of gamblers (recreational gamblers, support-seeking, treatment-seeking, and gamblers in self-help groups)	PAF (orthogonal rotation, % variance explained)	3 F structure supported with substantial cross-loading.
CFA
Miller et al. (2013)	33301	Integrated dataset of representative Canadian surveys	Not stated	Good fit for 1 F (CFI = .972, RMSEA = .059, loadings = .54–.72).
Lopez-Gonzalez et al. (2018)	659	Subsample of Spanish sports bettors	WLS	Good fit for 1 F (CFI = .997, RMSEA = .063, loadings = .77–.96).
Loo et al. (2011)	387	Student and community sample (Taiwan)	Not stated	Poor fit for 1 F (CFI = .81, RMSEA = .12), modified model (1-2, 2-3, 3-4, 5-8) fit better (CFI = .92, RMSEA = .08).
Boldero and Bell (2012)	370	Australian student sample	ML and WLS (Bayesian)	Supported 1 F model. ML models fit poorly, but WLS models fit well. Fit stats are not fully reported.
Griffiths and Nazari (2021)	429	Online sample of Iranian gamblers	ML	Good fit for 1 F (CFI = .974, RMSEA = .057, SRMR = .028, loadings = .64–.76).
Gorenko et al. (2022)	518	A subsample of older adults from the Quinte Longitudinal Study	ML with Bollen-Stine bootstrap	Good fit for 1 F (CFI = .996, RMSEA = .02, loadings = .41–.84).
Arcan et al. (2020)	182	Turkish student sample	WLS	Good fit for 1 F (CFI = .99, RMSEA = .075, loadings = .61–.73).
Maitland and Adams (2005)	4631	Data taken from Wiebe and Single (2002, unpublished)	ML	Good fit for 1 F (TLI = .953, CFI = .972, RMSEA = .041), improved for 2 F (TLI = .954, CFI = .974, RMSEA = .041).
Maitland and Adams (2007)	2498 (S1), 669 (S2), 2248 (S3)	Three Canadian general population surveys	ML	S1: Poor fit for 1 F (TLI = .888, CFI = .816, RMSEA = .078), better for 2 F (TLI = .888, CFI = .919, RMSEA = .078). S2: similar to S1 for 1 F (TLI = .906, CFI = .929, RMSEA = .107) and 2 F (TLI = .933, CFI = .952, RMSEA = .090). S3: Similar again for 1 F (TLI = .870, CFI = .902, RMSEA = .112) and 2 F (TLI = .912, CFI = .936, RMSEA = .092).
Barbaranelli et al. (2013)	1979	Representative Italian panel study	WLS	Good fit for 1 F (.99, RMSEA = .055, loadings = .83–.911).
Marmurek and Cooper (2023)	1280	A mixture of Canadian sports bettors and gamblers recruited online	WLS	Good fit for 1 F (CFI = .995, RMSEA = .075, loadings = .855–.965).
Ahmadi and Gorbani (2021)	211	Iranian student sample	Not stated	Good model fit for 1 F (CFI = .99, RMSEA = .01).
Wieczorek et al. (2021)	150	Polish gamblers recruited from venues and clinics	ML	Supported 1 F (CFI = .89, RMSEA = .36 with CI of .02–.14, SRMR = .01, loadings = .59–.77).
Tseng et al. (2023)	3740	Australian general population sample	ML with Bollen-Stine bootstrap	Supported 2 F (CFI = .92, RMSEA = .15).
Tabri and Wohl (2023)	3740	Same data as Tseng et al.	WLS	Good fit for 1 F (CFI = .995, RMSEA = .021) and 2 F (CFI = .996, RMSEA = .021), supported 1 F on bifactor (CFI = 1.000, RMSEA = .005).
Schellenberg et al. (2016)	932	Telephone survey of gamblers in Canadian province	WLS	Good fit for 1 F (CFI = .995, RMSEA = .023).
Frasheri and Shahini (2017)	1157	Sample of Albanian school students	WLS	Supported 2 F (CFI = .989, RMSEA = .051).
Onyedire et al. (2021)	252	Nigerian student sample	ML	Supported 1 F (CFI = .90, RMSEA = .05).
Currie et al. (2010)	12792	Split half of a mixture of Canadian general population surveys	ML	Supported 1 F (CFI = .972, RMSEA = .059).
Molander and Wennberg (2022)	598	Four populations of gamblers (recreational gamblers, support-seeking, treatment-seeking, and gamblers in self-help groups)	ML	Did not support 1 F (CFI = .948, RMSEA = .135, loadings = .68–.92). Conducted exploratory analysis (see EFA).
Auer et al. (2023)	10000	Gamblers recruited from Croatian online lottery operator	Not stated	1F inadequate fit (CFI = .944, TLI = .936, RMSEA = .10), Scree test and parallel analysis supported 1 F.
Cooper and Marmurek (2023)	1251	Same data as Marmurek and Cooper (2023)	WLS	Support for 1 F (RMSEA = .075, WRMR = 1.157, CFI = .995, TLI = .994) but stronger for 2 F (RMSEA = .065, WRMR = .968, CFI = .996, TLI = .995). 2 F showed limited criterion validity over 1 F.
Tabri et al. (2023)	308 (S1), 2008 (S2)	University students (S1) and a general population sample of a Canadian province recruited by an online panel (S2)	MLR	Configural invariance between 2 time points. Fit poor in S1 (CFI = .88, RMSEA = .06, SRMR = 10), improved with correlated residuals. Model fitted in S2 (CFI = .98, RMSEA = .02, SRMR = .03).
Akbari et al. (2023)	2390	Iranian adolescents (13–18) recruited via social media	WLS	Support for 1 F (RMSEA = .050, CFI = .994, TLI = .992, loadings = .92–.97).

Notes. FA: Factor Analysis; GLS: Generalized Least Squares; ML(R): (Robust) Maximum likelihood; MAP: (Velicer’s) Minimum Average Partial; PA: Parallel Analysis; PAF: Principal Axis Factoring; PCA: Principal Components Analysis; WLS(MV): Weighted Least Squares (with mean and variance adjusted statistics); CFI: Comparative Fit Index; TLI: Tucker Lewis Index (or NNFI) ; RMSEA: Root Mean Square Error of Approximation; SRMR: Standardized Root Mean Residual.

Table 2. Summary of sample sizes, PGSI scores, and distributions.

Dataset^a	N	M	S.D.	Skew	Kurtosis	α
BGPS2007	5,621	0.267	1.408	10.856	158.164	0.917
BGPS2010	5,706	0.288	1.453	9.776	128.550	0.907
NIPS2010	1,032	0.555	1.952	5.062	33.915	0.905
HSE2012	4,264	0.176	1.118	12.679	223.786	0.914
SHES2012	2,730	0.205	1.381	11.068	153.446	0.936
HSE2015	4,080	0.228	1.525	11.608	167.131	0.947
SHES2015	2,655	0.166	1.124	11.399	165.909	0.922
HSE2016	3,709	0.196	1.182	10.146	135.273	0.912
SHES2016	2,246	0.190	1.410	12.154	177.725	0.944
SHES2017	1,676	0.202	1.347	11.133	161.309	0.941
HSE2018	3,733	0.205	1.352	11.992	182.085	0.929
SHES2021	2,052	0.206	1.179	10.966	153.898	0.882
NSW2022-23	2,918	0.230	1.330	10.189	128.422	0.902
Aggregated Data	42,422	0.230	1.358	10.843	154.135	0.920

^a BGPS = British Gambling Prevalence Survey, NIPS = Northern Ireland Gambling Prevalence Survey, HSE = Health Survey for England, SHES = Scottish Health Survey, NSW = National Survey for Wales.

Table 3. Summary of model fit indices (mean and range) for the disaggregated models.

Model	Χ^2	df	Χ^2 p > .05	RMSEA	CFI	TLI	SRMR	Unbiased SRMR
1F CFA (MLR)	71.22 (19.26–126.16)	27	2	0.13 (0.08–0.19)	0.92 (0.86–0.97)	0.9 (0.82–0.96)	0.04 (0.03–0.06)	0.02 (0–0.04)
1 F CFA (WLS)	64.21 (28.54–146.42)	27	3	0.01 (0–0.02)	1 (1–1)	1 (1–1)	0.03 (0.02–0.04)	0.01 (0–0.03)
2 F CFA (MLR)	52.55 (15.46–84.36)	26	3	0.11 (0.07–0.15)	0.94 (0.89–0.98)	0.92 (0.84–0.97)	0.03 (0.02–0.05)	0.01 (0–0.03)
2 F CFA (WLS)	45.99 (21.41–93.28)	26	3	0 (0–0.02)	1 (1–1)	1 (1–1)	0.02 (0.01–0.04)	0.01 (0–0.03)
2 F ESEM (MLR)	39.42 (10.09–67.20)	19	3	0.10 (0.07–0.16)	0.96 (0.94–0.99)	0.93 (0.88–0.97)	0.03 (0.02–0.03)	0.02 (0–0.03)
2 F ESEM (WLS)	23.46 (14.57–33.76)	19	5	0 (0–0)	1 (1–1)	1 (1–1)	0.01 (0.01–0.02)	0.00 (0–0.01)
BI-ESEM + 1 F (MLR)	48.88 (11.20–126.99)	19	2	0.10 (0.07–0.16)	0.96 (0.94–0.99)	0.93 (0.88–0.97)	0.02 (0.02–0.03)	0.01 (0–0.02)
BI-ESEM + 1 F (WLS)	26.70 (14.57–39.67)	19	8	0 (0–0)	1 (1–1)	1 (1–1)	0.01 (0.01–0.02)	0.01 (0–0.01)
BI-ESEM, + 2 F (MLR)	65.97 (11.13–200.58)	12	4	0.08 (0.05–0.12)	0.99 (0.98–0.99)	0.96 (0.93–0.98)	0.01 (0.01–0.02)	0.01 (0–0.02)
BI-ESEM, + 2 F (WLS)	14.36 (8.36–19.92)	12	9	0 (0–0)	1 (1–1)	1 (1–1)	0.01 (0.01–0.02)	0.00 (0–0.01)

Table 4. Indices of model-based reliability for the CFA, ESEM, and BI-ESEM models (mean and range).

		MLR				WLSMV
Model	F	ΩH	H	FD	Ω	ΩH	H	FD	Ω
1 F CFA	1	0.91 (0.88–0.94)	0.97 (0.95–0.98)	0.94 (0.9–0.96)		0.94 (0.89–0.98)	0.99 (0.99–1)	0.99 (0.98–1)
2 F CFA	1	0.78 (0.68–0.86)	0.94 (0.92–0.96)	0.82 (0.71–0.88)	0.92 (0.88–0.95)	0.81 (0.7–0.89)	0.99 (0.98–1.04)	0.97 (0.92–1.04)	0.94 (0.89–0.97)
	2	0.91 (0.87–0.95)	0.97 (0.95–0.98)	0.92 (0.87–0.95)		0.92 (0.86–0.96)	0.99 (0.99–1.00)	0.99 (0.97–1.00)
2 F ESEM	1	0.23 (0.09–0.47)	0.92 (0.87–0.96)	0.80 (0.66–0.91)	0.92 (0.88–0.95)	0.90 (0.83–0.96)	1 (0.99–1)	0.99 (0.98–1)	0.93 (0.89–0.96)
	2	0.33 (0.12–0.49)	0.97 (0.93–0.99)	0.93 (0.83–0.98)		0 (0–0)	0.84 (0.73–1.12)	0.17 (0.11–0.23)
BI-ESEM + 1 F	1	0.92 (0.88–0.96)	0.97 (0.96–1.01)	0.94 (0.91–0.96)	0.92 (0.88–0.96)	0.93 (0.89–0.96)	1 (0.99–1)	0.99 (0.98–1)	0.93 (0.89–0.96)
	2	0 (0–0.01)	0.82 (0.68–1.49)	0.35 (0.23–0.74)		0 (0–0)	0.9 (0.74–1.5)	0.19 (0.11–0.28)
BIESEM + 2 F	1	0.9 (0.86–0.93)	0.98 (0.97–0.99)	0.94 (0.93–0.96)	0.93 (0.9–0.95)	0.93 (0.9–0.95)	1 (0.99–1.02)	0.99 (0.98–1)	0.94 (0.92–0.96)
	2	0.02 (0–0.05)	0.81 (0.71–0.9)	0.37 (0.29–0.46)		0 (0–0.01)	0.97 (0.81–1.23)	0.20 (0.12–0.33)
	3	0 (0–0.02)	0.77 (0.62–1.06)	0.27 (0.16–0.36)		0 (0–0.01)	1.2 (0.73–2.68)	0.26 (0.08–0.9)

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