Item bias and item response theory

“…is necessary to ensure that the same construct is measured across groups or time points, which is often referred to as measurement invariance (Drasgow, 1984; Holland & Wainer, 1993; Mellenbergh, 1989; Meredith, 1993; Meredith & Millsap, 1992; Millsap & Everson, 1993; Reise, Widaman, & Pugh, 1993).”

“The formal definition of measurement invariance (MI), according to Mellenbergh (1989) and Meredith (1993), states that MI holds when the probability of observed scale scores depends only on the estimated latent variable for the measure and not any other characteristic of the persons being measured…”

“Therefore comparison of the scores or the statistics associated with the observed and latent scores is valid only when an appropriate level of measurement invariance is established between groups (Mellenbergh, 1989; Meredith & Millsap, 1992; Millsap, 1997).”

“To further substantiate the interpretation of findings as indications of response shift, the associations between detected response shift effects and potential mechanism variables, according to response shift theory [36, 62], were also investigated.”

“That is, a set of observed variables is measurement invariant with respect to G populations if for any underlying latent trait value(s) g , its conditional distribution given that value(s), P( y j g ), is the same in all groups (cf. Mellenbergh, 1989).”

“Mellenbergh (1989), defining item bias as conditional dependence, suggests that statistical tests and indices based on item response theory may be used for detecting biased items when item characteristic curves of the two groups being tested do not coincide.”

“…misleading (Whisman et al., 2013) because it is ambiguous if the observed differences stem from the real gender differences in the unobserved (latent) construct, or they are due to structural differences (unequal conceptual perception of the tool’s items in males and females) (Mellenbergh, 1989).”

“[ 15 ] Although studies have established the validity and reliability of standardized alcohol abuse measures and diagnostic criteria in the general population, and provided support for single factor models, [16-26] the role of minority/majority based measurement bias in the instruments used to assess alcohol abuse in…”

“…which corrected observations for systematic effects induced by different observers and in doing so gave one of the first formal approaches to the notion of measurement bias, which has also become a fundamentally important concept in test theory (Lord, 1980;Mellenbergh, 1989;Meredith, 1993).”

“…invariance is critical to the validation of an instrument as it requires that the association of items and the constructs/latent factors independent from group membership or measurement occasion (Mellenbergh, 1989; Van De Schoot, Schmidt, De Beuckelaer, Lek, & Zondervan-Zwijnenburg, 2015).”

“This is nonuniform DIF (Camilli & Shepard, 1994; Mellenbergh, 1989).”

“…a psychological scale produces equivalent scores when administered to two groups of individuals who have the same latent trait level (e.g., positivity) but may differ in a characteristic unrelated to the latent trait, such as the presence or absence of a clinical diagnosis (Mellenbergh, 1989).”

“That measurement invariance does not hold implies that, whatever the intelligence test measures (Van der Maas et al. 2014), “intelligence” will have a different meaning for different individuals or groups of individuals (Mellenbergh 1989).”

“Identification of the same latent trait for all subgroups, such as gender and ethnicity, was identified by researchers as validity evidence in the form of measurement invariance (Mellenbergh, 1989).”

“…variable in question (i.e., self-concept), but also on another characteristic of the individual (i.e., reading achievement), we conclude that the dimensions of reading self-concept as measured by PISA, were not generalizable across levels of reading achievement (Bauer, 2017; Mellenbergh, 1989).”

“Formally, measurement invariance holds when the conditional distribution of the observed item scores is the same across subpopulations that are not part of the construct domain (Mellenbergh, 1989).”

“MI requires the association between the items/test scores (i.e., the raw scores from the instrument) and the latent factors to be independent of group membership (e.g., ethnicity) or measurement occasion (time; Mellenbergh, 1989).”

“An important prerequisite for such comparisons is that the same construct is being measured across groups or over time, that is, there is the assumption of measurement invariance across-groups (Mellenbergh, 1989) or over time (Millsap & Cham, 2013).”

“If this assumption is violated and measurement bias present, compar-Table isons may be invalid regardless of whether the scale has a high Chronbach ’ s alpha or reliability (Mellenbergh 1989; Meredith 1993).”

“The assumption of parameter invariance across subgroups—assessed as measurement invariance, differential item functioning, heterogeneity, or parameter stability in other contexts— underlies virtually all statistical tests (Bechger and Maris 2015; Hjort and Koning 2002; Hansen 1997; Mellenbergh 1989).”

“Psychometrics has been recognized as the approved term for the science behind psychological testing (Mellenbergh, 1989).”

“This phenomenon, acknowledged as differential item functioning (DIF) [12, 13], can markedly compromise the comparability patient-reported and proxy-reported measures and lead to biased comparisons [14].”

“The two most popular methods for testing measurement invariance of cross-cultural data are methods for detecting differential item functioning (DIF) [22], developed in the context of item response theory (IRT) [23], and Multiple-group CFA [24].”

“Measurement invariance analyses are used to test this assumption (for more details, see Mellenbergh, 1989; Meredith, 1993).”

“Como afirmam Camili e Shepard (1994) e Mellenbergh (1989), os índices DIF algumas vezes produzem resultados estatisticamente significativos na ausência do viés e em outras vezes não detectam o viés quando este se encontra presente em muitos itens, dada a circularidade do critério interno que…”

“…for the interpretation of a latent construct in the same manner between groups; thus, factorial invariance testing is a prerequisite to compare observed scores or latent factor means across groups (Mellenbergh, 1989; Meredith, 1993; Meredith & Millsap, 1992; Millsap, 1997; Reise et al., 1993).”

“Approaches for investigating how features S influence Z are investigating item bias [28], Differential Item Functioning (DIF) [29] and measurement invariance [30].”

“One type of such biases is called “item bias” which refers to an item’s inability to measure the same attribute across different groups (Mellenbergh 1989).”

“…or differential item functioning (DIF) is the possibility that individuals equal in their true levels of alcohol dependence, but from different groups (e.g., Caucasians and Hispanics), do not have identical probabilities of responding to questions concerning their alcohol use (Mellenbergh, 1989).”

“One of the strengths of FMM is that it allows for the assessment of measurement invariance (Mellenbergh, 1989; Meredith, 1993; Vandenberg & Lance, 2000) across latent classes in the population (Lubke & Muthén, 2005).”

“Mellenbergh (1989) gives a formal definition of measurement invariance.”

“Measurement invariance exists when the association between scores or items and latent factors (e.g. childhood adversity) is not dictated by group membership (e.g. sex, race; Mellenbergh, 1989).”

“Thus, the study of DIF within an IRT framework is a matter of comparing the item characteristic curves (ICCs) for the two sub-groups (that is male vs. female) (Hambleton and Swaminathan, 1985; Mellenbergh, 1989).”

“Bir başka deyişle, bireyin ölçek üzerinden aldığı gerçek puana sahip olma olasılığının üyesi olduğu herhangi bir gruptaki üyeliğinden bağımsız olma durumu anlamına gelmektedir (Mellenbergh, 1989; Horn ve McArdle, 1992).”

“…a historical summary see Millsap & Meredith 2007), the modern concept of testing the measurement invariance by means of factor analysis was shaped mostly by Mellenbergh (1989) and Meredith (1993), and the technical foundations for testing measurement invariance were laid down by Jöreskog (1971).”

“Measurement invariance analyses provide evidence that differences in test scores reflect true latent variable differences than group differences based on measurement bias [21,22].”

“differ in terms of a characteristic other than the latent trait, in this case, first language (Mellenbergh, 1989).”

“This test is omnibus because it does not distinguish between uniform and nonuniform DIF (see definitions in Mellenbergh, 1989 and Camilli & Shepard, 1994 , p.”

“An item (question) shows DIF when the probability of choosing a specific response differed significantly across the groups of interest conditional on the latent trait that the item is measuring.([40,41]) In an iterative fashion,([38]) DIF analysis was done by checking the modification indices (MI) for each of the 8 po…”

“Variousmethods havebeenproposedtodetectthistypeofbias[109],[110], [111].”

“Measurement invariance occurs when items, or a test, measure the same latent construct in the same way in different groups of people (Mellenbergh, 1989; Meredith, 1993).”

“MI is achieved when latent construct(s) (e.g., cognitive functioning, depression) are measured equivalently and comparably across groups (e.g., ethnicity, SES), test modes (e.g., paper, computer), or time points (Drasgow, 1984; Mellenbergh, 1989; Somaraju et al., 2022).”

“However, item parameters may differ across groups, a phenomenon known as differential item functioning (DIF [15,16]) in the literature.”

“An item k is measurement invariant when a male or female with the same latent trait θ has the same probability of a certain response (Mellenbergh, 1989; Millsap and Everson, 1993), that is, bk1 = bk2.”

“DIF is a term that stems from education testing and happens when persons of equal capability or intelligence arrive at different capability or intelligence scores based on the specific wording of an item.”

“From a statistical vantage point, this means that there must be equivalence between the mathematical functions that associate the factors (latent variables) with the observed variables or items (Mellenbergh, 1989).”

“Mathematically, the assumption of MI for latent constructs requires the independence of conditional probability distributions of the observed scores (Mellenbergh, 1989).”

“A measure is considered invariant when the association of a test item and its latent factor do not depend on membership within a particular group, or a particular time of measurement (Mellenbergh, 1989).”

“The Item response theory (IRT) [17], also called item characteristic curve, is a method used to explore the relationship between participants’ responses to different measurable items and their underlying latent traits.”

“DMF tek biçimli ve tek biçimli olmayan olmak üzere iki farklı şekilde görülebilir (Camilli ve Shepard, 1994; Mellenbergh, 1989).”

“We say that X shows measurement invariance in relation to W and V if and only if P.XjW; V / D P.XjW/; (1) for all X, W, and V (Lord, 1980; Mellenbergh, 1989; Meredith & Millsap, 1992).”

“The measurement is invariant if two people with the same level of a latent trait achieve the same test score (Mellenbergh 1989).”

“(Mellenbergh, 1989; Meredith, 1993; Millsap, 2011; Shealy & Stout, 1993; Vandenberg & Lance, 2000).”

“Measurement bias refers to a situation where there is variability in the observed test scores that cannot be entirely attributed to true changes in the measured construct and that is not merely the result of random measurement errors [37].”