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The object detection logic of latent variable technologies

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Abstract

Endemic to theoretical and applied psychometrics is a failure to appreciate that the logic at root of each and every latent variable technology is object detection logic. The predictable consequence of a discipline’s losing sight of an organizing logic, is that superficiality, confusion, and mischaracterization are visited upon discussion. In this paper, I elucidate the detection logic that is the foundational, and unifying, logic, of latent variable technology, and discuss and dissolve a number of the more egregious forms of confusion and mischaracterization that, consequent upon its having been disregarded, have come to infect psychometrics.

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Notes

  1. For an elucidation of the manner in which the ERC is presupposed in various of the methodological orientations indigenous to the social and behavioural sciences, see Maraun et al. (2008), wherein the ERC is referred to as the Augustinian Conception of Reality.

  2. Those within the class of the unobservable-phenomena such as “…a person's anxiety, extraversion, intelligence, or goal orientation” (Strauss 1999, p. 19), “…general intelligence…” (Borsboom 2008, p. 27), and “…social class, public opinion or extrovert personality…” (Everitt 1984, p. 2) referred to, variously, and among others, as latent constructs (e.g., Lord and Novick 1968), latent variables (e.g., Green 1954; Lazarsfeld 1950), latent concepts (Bollen 2002), underlying abilities (Lord 1952), underlying traits (Lord 1953), hypothetical variables (e.g., Green, 1954, p. 725), and latent traits (Birnbaum 1968).

  3. "It would seem that in general the variables highly loaded in a factor are likely to be the causes of those which are less loaded, or, at least that the most highly loaded measure-the factor itself-is causal to the variables that are loaded in it" (Cattell 1952, p. 362).

  4. "And what we want to learn is not so much F i-scores in AM solution-range most closely aligned with scores in P on causal sources of Z as the non-extensional nature of these causal variables" (Rozeboom 1988, p. 225).

  5. "If a causal conjecture substantively entails the existence of a taxon specifying (on theoretical grounds) its observable indicators, a clear-cut non taxonomic result of taxometric data analysis discorroborates the causal conjecture"(Meehl 1992, p. 152).

  6. "To use Guttman's measure of indeterminacy in factor analysis, we need not assume that the factors generating the data [italics added] on the observed variables…" (Mulaik 1976, p. 252). "which set of variables actually are the factors that generated the data [italics added]…"; "He then establishes a set of empirical operations that will measure that causal factor [italics added]…" Later in the same paper, in considering the idea of factors as constructed variates, he states that "such artificial variables in x could not serve as causal explanations of the variables in n" (Mulaik 1976, p. 254).

  7. "If, in the first place, we are willing to regard the factor model as describing an aspect of the real world whereby unobserved processes give rise [italics added] to "observable" random variables, it is then a contradiction to suppose that those processes are not unique. It is another contradiction to suppose that they are known… In short, most accounts of the fundamental factor model use the non-mathematical qualifier "unobservable" to describe the common factor scores. It is not yet proven that it is philosophically naive to do this." (McDonald 1972, p. 18).

  8. "The factorial methods were developed primarily for the purpose of identifying the principal dimensions or categories of mentality…" (Thurstone 1947, p. 55).

  9. "The task of isolating the independent aspects of experience has been a difficult one. Armchair methods dominated by deductive logic rather than by observation led to the faculty psychologies, traditionally unacceptable to modern psychology. Direct observation has likewise failed to arrive at any set of unitary traits which even approach a universal acceptance. Factor analysis or some similar objective process had to be brought into the search for the unitary traits of personality [italics added]" (Guilford 1954, p. 470).

  10. "To obtain a more precise definition of attitude, we need a mathematical model that relates the responses, or observed variables, to the latent variable" (Green 1954, p. 725).

  11. "In using the common factor model, then, with rare exceptions the researcher makes the simple heuristic assumption that two tests are correlated because they in part measure the same trait, rather than because they are determined by a common cause, or linked together in a causal sequence, or related by some other theoretical mechanism. It is a consequence of this heuristic assumption that we interpret a common factor as a characteristic of the examinees that the tests measure in common, and, correlatively, regard the residual (the unique factor) as a characteristic of the examinees that each test measures uniquely" (McDonald 1981, p. 107); "…I am describing the rule of correspondence which I both recommend as the normative rule of correspondence, and conjecture to be the rule as a matter of fact followed in most applications, namely: In an application, the common factor of a set of tests/items corresponds to their common property" (McDonald 1996, p. 670).

  12. "..the widely accepted aim of factor analysis, namely, the interpretation of a common factor in terms of the common attribute of the tests that have high loadings on it…"; "what attribute of the individuals the factor variable represents" (McDonald and Mulaik 1979, p. 298).

  13. See Maraun (2003) for a detailed analysis of this story, wherein it is called The Central Account.

  14. "The scale was originally designed to tap into a single source of variance…" (Hoyle and Lennox 1991, p. 511); "…in the Big Seven, Extraversion and Neuroticism are called Positive Emotionally and Negative Emotionally, respectively, in recognition of the emotional core of these higher order factors" (Benet and Waller 1995, p. 702).

  15. E.g., "…for the study of individual differences among people, but the individual differences may be regarded as an avenue of approach to the study of the processes which underlie [italics added] these differences" (Thurstone 1947, p. 55); "Latent variables can be more or less latent. (i) Firstly, they can be completely latent, unknown, hidden, invisible, undercover [italics added], unmanifested and their scientific purpose is as obscure as the LVs themselves and concepts…" (Lohmoller 1989, p. 81).

  16. E.g., "…"genetic composition" of a herd of cattle cannot be measured directly, but the effects of this composition can be studied through controlled breeding…Each postulates constructs that are not directly measurable and each observes phenomena that manifest these latent constructs but also exhibit fluctuation due to other factors…" (Lord and Novick 1968, p. 14).

  17. I do not view the logic that I, herein, describe as “a way of conceptualizing latent variable technologies”, but, rather, as, uncontroversially, the logic on which these technologies are founded.

  18. For an extended discussion of this issue, see Maraun (2003), Myths and Confusions: Psychometrics and the Latent Variable Model.

  19. See Michell (2012), in regards the general issue of the conditions that must be satisfied in order that a variable have quantitative character.

  20. Or, in the event that rmsea-style thinking is adopted, [H0: D(γ,\(\varOmega_{ulf}\)) ≤ c, H1: D(γ,\(\varOmega_{ulf}\)) > c], wherein D is a distance measure, and c is a positive number.

  21. Note: the multivariate normality of X is not a side condition (i.e., it is not required in order that GP ulf be true), but, rather, a statistical assumption attendant to a particular application of maximum likelihood machinery.

  22. e.g., a set of p quasi-continuous variables that happen to be undimensional in the sense of quadratic factor analysis, is 2-dimensional in the sense of linear factor analysis [and, for that matter, p dimensional in the classical euclidean sense (the sense of principal component analysis)].

  23. Of a type either disconfirmatory, confirmatory, or both, depending on the logical type of GP LS* .

  24. The tool of detection that is an implementation of this single proposition, having been rapidly mythologized to the status of general, open-ended, data analytic "technique."

  25. Paul Meehl has made this point on many occasions. His belief in the necessity of multiple detectors for a given latent structure was the reason that he invented his multiple consistency tests strategy for use in the detection of the taxonomic latent structure (cf. Meehl 1995).

  26. cf. Linear factor analytic technology and the difficulty factor problem (see, especially, McDonald 1967).

  27. When the diprotic acid contained in the limus enters an alkaline solution, the hydrogen ions it releases form, with the base, a blue-coloured conjugated base.

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  1. Department of Psychology, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Michael Maraun

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Maraun, M. The object detection logic of latent variable technologies. Qual Quant 51, 239–259 (2017). https://doi.org/10.1007/s11135-015-0303-0

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