Introduction
This paper addresses measurement issues in the classification and identification of children with learning disabilities (LD). It will address different identification models, including those based on two tests at the same point in time (epitomized by the IQ- discrepancy model), a single test/time point (epitomized by the low achievement model), and by a single test at multiple time points over time (epitomized by the response to intervention model). In addressing these measurement issues, it is important to recognize that LD is a construct, or latent variable, that is always imperfectly measured. Controversies about measurement, however, do not mean that the underlying construct is not real. From a validity viewpoint, the major question is whether different approaches to measurement identify a unique group of children identifiable as LD who represent the construct of unexpected underachievement, the key component of most conceptualizations of LD (Lyon et al., 2001). If there are problems with the reliability of how unexpected underachievement is measured, such that the underlying psychometric model is not suitable for identifying a unique group of children, then the validity issue is moot. Valid classifications hinge on reliable measurement systems, and there can be no validity without reliability. In other words, reliability sets an upper limit on validity (Francis et al., in press).
Measurement issues are not independent of classification. In fact, how LD s are defined and therefore identified reflects a classification indicating how those with LD are similar and dissimilar (i.e., unique) relative to other children and adults (Fletcher & Morris, 1986; Morris & Fletcher, 1988). Thus, while it is relatively easy to demonstrate that LD is a valid classification when comparisons are made to children with mental retardation, typical achievers, or across different academic types of LD (e.g., reading versus math disability), it is harder to validate classifications that separate subgroups within major academic domains, such as an IQ-Achievement discrepancy model of classification from a Low-Achievement model (see Fletcher et al., 2002). It is not that the competing systems (by definition) do not identify distinct individuals, but that the individuals so identified do not differentiate on other important dimensions relevant to the construct of interest. Different approaches simply do not identify unique subgroups, partly because of problems with the underlying measurement models (see Francis et al., in press; Stuebing et al., 2002).
It is possible that measurement problems stem from the dimensional nature of LD. Some studies of children with LD (in reading) have suggested that the distribution of achievement test scores is not normal, and identified discontinuities that could be used as a cut point (Miles & Haslum, 1986; Rutter & Yule, 1975; Wood & Grigorenko, 2001). However, a series of epidemiological, population-based studies of reading and math disabilities in children have shown consistently that reading (Jorm et al., 1986; Rodgers, 1989; Shaywitz et al., 1992; Silva et al., 1985; Stevenson, 1988) and math (Lewis, Hitch, & Waller, 1994; Shalev et al., 2000) skills are normally distributed in our population. There is no consistent evidence for bimodality or other forms of non -normality in population distributions of these skills. Even genetic studies are not consistent with the presence of qualitatively different characteristics associated with the heritability of reading and math disorders; the assumption of normal variation is pivotal for this type of research (Gilger, 2002). These observations are important because as normally distributed traits that exist on a continuum, there are no natural demarcation points that differentiate individuals with reading or math disabilities from those who are not defined as disabled (Shaywitz et al., 1992). Consequently, it is difficult to determine cut points for accurately and reliably identifying individuals with LD in the absence of external criteria (e.g., functional outcomes), which has rarely been attempted.
The dimensional nature of LD complicates the use of single cut points or boundaries on a continuous univariate or bivariate distribution and makes identification based on such static measurement models derived from a single assessment unreliable in predictable ways (Francis et al., in press; Stuebing et al., 2002). This problem with the use of a single static assessment in classification does not mean that LD is simply underachievement. What it means is that the measurement system is incapable of adequately reflecting the phenomenon of interest because the measurement model is under-identified. Put another way, the system carries insufficient information about the phenomenon of interest to allow for reliable and valid classification of individuals along the unobservable dimension(s) of interest. This problem would be partly ameliorated if LD was a manifest concept, that is, if LD were a phenomenon that is directly observable in the behavior of affected individuals. But LD is not directly observable; rather LD is a latent construct in the same sense that achievement and intelligence are latent constructs. Thus, LD must be inferred from the observed pattern of relations among manifest operations. The more observed relations that we have at our disposal, the more information we have on which to base our inference of LD, the more reliable and valid that inference becomes, and the finer the distinctions that can be supported by the system.
Dimensional distinctions are more fine-grained than class-based distinctions; class-based distinctions are more fine-grained when one or more class sizes are small. When the measurement system is underidentified, the only solution is to expand the dimensionality of the measurement system to increase the number of observed relations. In that sense, it is the absence of some type of external criterion that makes it difficult to identify a unique subgroup of underachieving individuals consistent with the construct of LD when identification is based on a single assessment at a single time point. Adding external criteria increases the dimensionality of the measurement system and makes latent classification possible, even when the external criteria are themselves imperfect.
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