| H1, H2, H3 | 3847 male criminal offenders 1219 female criminal offenders | PCL‑R | IRT, CFA | Two-factor, four-facet hierarchical model with an additional third-order factor | The CFA model yielded acceptable fit for both male and female subsamples, indicating CI. DIF was found for 12 items. Latent mean scores were higher for men than for women (estimate = −0.45, p < 0.001) |
| H1 | 200 community and 176 prison methadone program participants (65% male; Mage = 32.5 [SD = 6.2, range 19–49]) | PCL‑R | CFA | Two-factor model | The model fit both male and female subsamples poorly |
| H1 | 4865 male (Mage = 20.03 [SD = 7.30]) offenders 1099 female offenders (Mage = 17.24 [SD = 6.87]) | PCL‑R | CFA | Four-correlated factors model | The model fit both male and female subsample well, indicating CI. Discrimination (loadings) and extremity (intercept) parameters indicated a sex bias on three or two items, respectively |
| H1 | a) 473 male released psychiatric patients (Mage = 29.8 [SD = 6.3]) b) 356 female released psychiatric patients (Mage = 29.9 [SD = 6.1]) | PCL‑R | CFA | Four-factor model | Model fit was acceptable for both samples, indicating CI |
Klein Haneveld et al. ( 2022) | H1, H2, H3 | 110 female and 147 male criminal offenders | PCL‑R | MGCFA | Two-factor, four-facet hierarchical model with an additional third-order factor | Full CI was obtained. Partial MI held with one item and partial SI held with two items differing between sexes. Females scored significantly lower than males on all four facets with the largest effect on the antisocial facet and the smallest effect on the interpersonal facet. (interpersonal, estimate = −0.549, p = 0.002; affective, estimate = −0.689, p < 0.001; lifestyle, estimate = −0.612, p < 0.001, antisocial, estimate = −1.498, p < 0.001) |
Windle and Dumenci ( 1999) | H1, H2, H3 | 481 male and 321 female alcoholic psychiatric inpatients (Mage = 34.41 [SD = 7.71]) | PCL‑R | MGCFA | Two-factor model | CI fully held, partial MI held with one item differing between sexes, and partial SI held with three items differing between sexes. No latent mean differences on either of the two factors were found (p > 0.10) |
Strand and Belfrage ( 2005) | H1, H2 | 129 female and 499 male Swedish offenders (Mage = 36 [SD = 11, range 18–68]) | PCL:SV | EFA and IRT | – | EFA revealed a two-factor solution for males and a three-factor solution for females. DIF was found for 5 items |
| H1 | 1) 25 male and 25 female undergraduate students (Mage = 24.8 [SD = 6.7]) 2) 25 male and 25 female undergraduate students (Mage = 20.2 [SD = 2.4]) 3) 25 male and 25 female undergraduate students (Mage = 21.6 [SD = 5.1]) | PCL:SV | Congruence co-efficients | Two-factor model | A clear two-factor solution was not obtained in either sample. The congruence coefficient indicated that factors were not satisfyingly similar between sexes (rc = 0.83 for the first factor and rc = 0.34 for the second factor) |
| H1 | 385 male and 180 female adults (Mage = 27.5 [SD = 6.15, range 18–45]) | PCL:SV | CFA | A two-factor and a four-facet model | Both models exhibited adequate fit to the data for both sexes, indicating CI |
| H2, H3 | Community sample of 196 males and 318 females (Mage = 31.0 [SD = 6.1]) | PCL:SV | MGCFA | Four correlated factors model | SI model exhibited good fit to the data. Other levels of invariance were not tested. Observed PCL:SV scores were higher for men (M = 3.53 [SD = 3.79]) than for women (M = 2.16, [SD = 3.23]) with a small effect size (d = 0.30) |
| H1, H2 | 870 psychiatric inpatients (58% male, Mage = 30 [SD = 6]) | PCL:SV | MGCFA | Three-factor model | CI and MI held across sexes. SI was not tested |
| H1, H2 | 1414 individuals endorsing serious criminal histories (62% male, Mage = 30.34 [SD = 7.39, range 18–73]) | CAPP-LRS self-report | MGCFA | First-order three-factor model | CI held, partial MI held, but SI could not be established |
| H1, H2, H3 | Community sample of 719 individuals (51% female, age range 18–> 70) | CAPP-LRS self-report | MGCFA | Bi-factor model with one general factor and three bi-factors | CI held, partial MI held with 12 items differing between sexes. Partial SI held with 7 items differing between sexes. Men scored significantly higher than women on the general factor (z = 8.14, p < 0.001, d = 0.68) and the three bi-factors boldness/emotional stability (z = 2.84, p = 0.005, d = 0.28), emotional detachment (z = 4.86, p < 0.001, d = 0.60), and disinhibition (z = 1.97, p = 0.049, d = 0.18) |
| H1 | 840 military personnel (81.2% male, Mage = 27.08) | LSRP | CFA | 26-items three-factor model, 19-items two- and three-factor models | The models all provided acceptable fit for both male and female subsamples, suggesting CI for all models |
| H1 | Community sample of 277 males and 463 females (Mage = 36.52 [SD = 12.87, range 18–65]) | LSRP | Congruence co-efficients | – | Congruence coefficients supported the fit of a three-factor model across sex groups (rc values of 0.97, 0.94, and 0.94 for factors 1, 2, and 3, respectively), indicating CI |
| H1, H2 | Mixed subsample of 1746 undergraduate students | LSRP | MGCFA | Two-factor model | Partial MI with one item loading differing between sexes. No further analyses were reported |
| H1, H2 | 1) 558 male prison inmates (Mage = 32.31 [SD = 9.65, range 18–66]) 2) 202 male and 200 female college students (Mage = 19.39 [SD = 3.37, range 18–56]) | LSRP | CFA, MGCFA | One-factor model, two different two-factor models, two different three-factor models | CFAs did not yield adequate fit for any of the models. Two models were modified and yielded adequate fit afterwards. CI and MI were obtained for the revised three-factor model. SI was not examined |
| H2 | 1516 college students (58.9% female, Mage = 18.68 [SD = 1.8, range 17–46]) | LSRP | IRT | – | Seventeen items displayed DIF |
Hauck-Filho and Teixeira ( 2014) | H2 | Brazilian community sample of 644 females and 240 males (Mage = 28.58 [SD = 10.55]) | LSRP | IRT | – | Three items displayed DIF with negligible differences in difficulty estimates |
| H1, H2 | 428 female and 178 male undergraduate students (Mage = 19.90 [SD = 3.48, range 18–48]) | Hare SRP | MGCFA | Four-factor model | Full MI and SI between sexes were supported |
| H1, H2 | 19,183 females and 13,833 males from 58 nations (Mage = 21 [range 18–91]) | SRP‑E (with 19 instead of 21 items) | CFA; MGCFA | Four-factor model | CFAs supported good model fit for both sexes. Full CI, MI and SI across sex were supported |
| H1, H2, H3 | 481 workers recruited from MTurk (61.3% female, Mage = 36.10 [SD = 12.58]) | SRP-SF, TriPM | MGCFA | SRP: four-factor model TriPM: three-factor model | No MI was obtained for the SRP-SF. MI and SI held for the TriPM. Latent means were not equivalent (∆Χ2 = 79.72, p < 0.001). Hereby, women scored lower than men on all three factors (boldness, t (474) = 5.874, p < 0.001; meanness, t (474) = 8.262, p < 0.001, and disinhibition, t (474) = 3.898, p < 0.001) |
| H1, H2 | 1) 384 college students (65.1% female, Mage = 19.3 [SD = 1.67, range 18–34]) 2) 848 college students (45.8% female, Mage = 20.71 [SD = 4.24, range 18–57]) 3) 1012 college students (57.3% female, Mage = 19.67 [SD = 1.25, range 18–22]) 4) 283 22-year-old men from the Pitt Mother & Child Project | SRP-SF | CFA, MGCFA | Four-correlated factor model, bi-factor model with one general factor and four bi-factors | CFAs for the four-correlated factor model yielded inadequate fit for men, but good fit for women. The four bi-factor model yielded good fit for both sexes. CI was not established for the four-correlated factor model but for the bi-factor model. At the scalar level there is evidence for the presence of SI, the Χ2-test, however, was significant |
| H1, H2, H3 | 590 undergraduate students (65% females, Mage females = 20.52 [SD = 3.89], Mage males = 21.07 [SD = 4.92]) | SRP-SF | MGCFA | Four-factor model | Full CI and full SI were obtained. MI was not examined. Men (M = 62.10, SD = 15.95) obtained higher observed SRP-SF total scores than women (M = 51.97, SD = 15.19; F(1, 587) = 65.85, p < 0.001) with a small effect size (η2 = 0.10) |
| H2 | 348 male and 704 female college students (age range 18–49) | PPI‑R | IRT | – | Eighty items (61.1%) displayed significant DIF between men and women |
| H1, H2 | 145 male and 215 female undergraduates (Mage = 18.95 [SD = 1.42, range 18–28]) | PPI‑R | CFA; MGCFA | One-factor, two-factor, and three-factor model | In separate CFAs the one-factor and two-factor model yielded good fit for the female sample and barely acceptable fit for the male sample, while for the three-factor model fit was modest for both groups. Partial MI was attained for the one- and the two-factor model with two items and one item differing between sexes, respectively. The partially constrained three-factor model fit the data poorly. No further constraints were applied |
| H1 | Community sample of 869 females and 378 males (Mage = 19.32 [SD = 2.31, range 17–51]) | PPI-SF | CFA | Eight-factor model | The model fit both male and female subsamples poorly |
| H2 | 1) 138 male and 269 female students 2) 272 males and 258 females recruited from MTurk (Mage = 30.3 [SD = 12.2, range 18–75]) | TriPM | IRT | – | Thirty-four items (61%) displayed significant DIF between men and women |