Application of the Double Monotonicity Model to Polytomous Items

Abstract

Abstract. This paper investigates the item scalability of the Beck Depression Inventory (BDI) in 252 subjects; 126 with and 126 without eating disorders. To do so, an order was established regarding the BDI items according to the clinical characteristics of the subjects with eating disorders. The nonparametric Item Response Theory (NIRT) model was applied to evaluate Monotone Homogeneity and Double Monotonicity of items, as well as the reliability of the scale in both groups. The results show that the order of the items is satisfied in the group with eating disorders, but not in the control group. Therefore, the results obtained allow the ordering of depression scores of subjects with eating disorders according to their clinical characteristics. This order is not valid for the depression scores of subjects who did not have eating disorders. It should be noted that the application of the Double Monotonicity model to polytomous items provides new and relevant information when compared to the data provided by the Classical Test Model. In addition, it is very useful for other items and subjects having certain characteristics.

Examination of Polytomous Items’ Psychometric Properties According to Nonparametric Item Response Theory Models in Different Test Conditions

“…In addition, LCRC reliability values, estimated according to MHM of tests with polytomous items, were high. This finding supports that of Rivas et al (2005), who suggested achieving tests with high reliability by using scaling according to MHM.…”

“…In these studies, which generally use large samples and long tests, a limited number show that NIRT is useful in short tests and small samples-the observed advantage of NIRT over PIRT (Aderka et al, 2013;Galindo Garre et al, 2014;Laroche et al, 1999;Lee et al, 2009;Meijer & Baneke, 2004;Palm & Strong, 2007;Patsula & Gessaroli, 1995;Rivas et al, 2005;Sijstma et al, 2008;Sueiro & Abad, 2011;Young et al, 2003).…”

“…Here, studies conducted within the NIRT framework were examined, and the following are studies in which various scales' psychometric properties were examined: Bedford, Watson, Henry, Crawford, andDeary (2011), Galindo Garre et al (2014), Laroche, Kim, and Tomiuk (1999), Palm and Strong (2007), Pope (1997), Rivas, Bersabé, and Berrocal (2005), Roosen (2009), Sach, Law, andChan (2003), Stewart, Watson, Clark, Ebmeier, and Deary (2010), Štochl, Jones, and Croudace (2012), Valois, Frenette, Villeneuve, Sabourin, and Bordeleau (2000), and Young, Blodgett, and Reardon (2003); comparison of PIRT and NIRT with regards to estimating scales' psychometric properties: Dyehouse (2009), Gouge (2008), Kogar (2015), Meijer and Baneke (2004), Patsula and Gessaroli (1995), Sijtsma et al (2008), andZhou (2011); studies in which short versions of scales are being developed: Aderka et al (2013), Aljubaily (2010), Gouge (2008), Khan, Lewis, andLindenmayer (2011), Sodano, Tracey, andHafkenscheid (2014); studies in which model-data fit in PIRT models are explored to NIRT models: Douglas and Cohen (2001), Emons (2008), Lee (2007), Lee et al (2009), Liang, Wells, andHambleton (2014), Sueiro andAbad (2011), andSyu (2013) and studies in which items are chosen according to NIRT in simulative test conditions: Straat, van der Ark, and Sijtsma (2014). In these studies, which generally use large samples and long tests, a limited number show that NIRT is useful in short tests and small samples-the observed advantage of NIRT over PIRT …”

Psychopathy in adolescent female offenders: an item response theory analysis of the psychopathy checklist: youth version

“…Specifically, examining eigenvalues and variance accounted for by each factor can be illustrative. For the current study, the first three eigenvalues (and variance accounted for) for the PCL-YV data were 6.504 (39.2%), 1.504 (6.04%), and 1.34 (3.02%), indicating, based on the index UNIDI ¼ ( 1 -2 )/( 2 -3 ) > 5 (Rivas, Bersabe, & Berrocal, 2005), strong support for unidimensionality. Reliability estimates can also be helpful in determining the coherence of the construct.…”

An examination of the Psychopathy Checklist: Youth Version (PCL:YV) among male adolescent offenders: An item response theory analysis.

“…The first three eigenvalues were 5.90, 1.70, and 1.33, respectively, accounting for 29.48%, 8.48%, and 6.62% of the variance. According to the UNIDI index—(λ 1 – λ 2 )/(λ 2 – λ 3 ) > 5 (Martínez Arias, 1995, p. 297)—results of the PCA demonstrated very good support of unidimensionality (Rivas, Bersabe, & Berrocal, 2005). Inter-item reliability (Cronbach’s α = .88) estimates indicated good internal consistency for the total PCL:YV items.…”