What If We Took Our Models Seriously?

1. What If We Took Our Models Seriously? Estimating Latent Scores in Individuals W. Joel Schneider Department of Psychology

5. [E]very individual is a singularity, a one-time existing being, nowhere else and never before present. To be sure, certain law-like regularities apply to him, certain types are embodied in him, but the individual is not exhausted by these laws and types; there remains ever something more, through which the individual is distinct from others who conform to the same laws and types. William Stern 1871–1938

6. And this last kernel of being, which reveals the individual to be thus and so, distinct from all others, is not expressible in the language of scientific concepts, it is unclassifiable, incommensurable. In this sense, the individual is a limiting concept, toward which theoretical investigation strives but can never reach; it is, one could say, the asymptote of science. William Stern 1871–1938

7. A Revolutionary Idea Francis Galton (1822-1911) Karl Pearson (1857-1936) circa 1909

8. Up to 1889 [scientists] had thought only in terms of causation, in [the] future they were to admit another working category, that of correlation, and thus open to quantitative analysis wide fields of medical, psychological and sociological research. Karl Pearson

9. […]we realize to-day how little progress in that direction was possible because [earlier scholars] lacked the key—correlation—to the treasure chamber. Karl Pearson

10. […] Galton turning over two different problems in his mind reached the conception of correlation: A is not the sole cause of B, but it contributes to the production of B; there may be other, many or few, causes, some of which we do not know and may never know. Karl Pearson

11. Are we then to exclude from mathematical analysis all such cases of incomplete causation? Galton’s answer was: “No, we must endeavor to find a quantitative measure of this degree of partial causation.” Karl Pearson

12. This measure of partial causation was the germ of the broad category—that of correlation, which was to replace not only in the minds of many of us the old category of causation, but deeply to influence our outlook on the universe. Karl Pearson

13. X Y d.Y

14. X Y d.Y

15. X d.Y Y

16. d.Y Y X

17. If X = ? If X = 100 d.Y Y X

18. If X = ? If X = 100 d.Y X Y

19. If X = 70 Y

20. Does Block Design measure visual-spatial ability?

23. s.SI .43 d.Gc .82 Similarities e.SI .37 .54 s.VO .34 .88 Vocabulary e.VO .33 .74 s.CO Gc .51 Comprehension e.CO d.Gv .44 .84 s.IN .39 .84 Information .74 e.IN .37 s.WR .50 d.Ind .32 Word Reasoning e.WR .45 s.PCm .64 .63 .40 Picture Completion e.PCm .46 .40 s.BD .37 .85 g .78 Gv Block Design e.BD .37 .32 .89 s.MR .59 Matrix Reasoning .79 e.MR Induction .33 .48 s.PCn .64 .86 Picture Concepts Arithmetic e.PCn .64 .42 s.DS .69 .63 Digit Span e.DS .55 .51 .35 Gsm .36 .72 s.LNS .62 Letter-Number Seq. s.AR e.AR e.LNS .51 .42 s.CD .46 .29 Coding d.Gsm e.CD .39 s.SS .53 .80 Gs Symbol Search .84 e.SS .46 .54 s.CA .73 Cancellation d.Gs .50 e.CA .46

24. s.SI .43 d.Gc .82 Similarities e.SI .37 .54 s.VO .34 .88 Vocabulary e.VO .33 Gc .74 s.CO Gc .51 Comprehension e.CO d.Gv .44 .84 s.IN .39 .84 Information .74 e.IN .37 s.WR .50 d.Ind .32 Word Reasoning e.WR .45 s.PCm .64 .63 .40 Picture Completion e.PCm .46 .40 s.BD .37 .85 g Gv .78 Gv Block Design e.BD .37 .32 .89 s.MR .59 Matrix Reasoning .79 e.MR Induction Induction .33 .48 s.PCn .64 .86 Picture Concepts Arithmetic e.PCn .64 .42 s.DS .69 .63 Digit Span e.DS .55 .51 .35 Gsm Gsm .36 .72 s.LNS .62 Letter-Number Seq. s.AR e.AR e.LNS .51 .42 s.CD .46 .29 Coding d.Gsm e.CD .39 s.SS .53 .80 Gs Symbol Search .84 e.SS .46 .54 s.CA .73 Cancellation d.Gs .50 e.CA .46

25. s.SI .43 d.Gc .82 Similarities e.SI .37 .54 s.VO .34 .88 Vocabulary e.VO .33 .74 s.CO Gc .51 Comprehension e.CO d.Gv .44 .84 s.IN .39 .84 Information .74 e.IN .37 s.WR .50 d.Ind .32 Word Reasoning e.WR .45 s.PCm .64 .63 .40 Picture Completion e.PCm .46 .40 s.BD .37 .85 g .78 GvGf Block Design e.BD .37 .32 .89 s.MR .59 Matrix Reasoning .79 e.MR Induction .33 .48 s.PCn .64 .86 Picture Concepts Arithmetic e.PCn .64 .42 s.DS .69 .63 Digit Span e.DS .55 .51 .35 Gsm .36 .72 s.LNS .62 Letter-Number Seq. s.AR e.AR e.LNS .51 .42 s.CD .46 .29 Coding d.Gsm e.CD .39 s.SS .53 .80 Gs Symbol Search .84 e.SS .46 .54 s.CA .73 Cancellation d.Gs .50 e.CA .46

26. s.SI .43 d.Gc .82 Similarities e.SI .37 .54 s.VO .34 .88 Vocabulary e.VO .33 Gc .74 s.CO Gc .51 Comprehension e.CO d.Gv .44 .84 s.IN .39 .84 Information .74 e.IN .37 s.WR .50 d.Ind .32 Word Reasoning e.WR .45 s.PCm .64 .63 .40 Picture Completion e.PCm .46 .40 s.BD .37 .85 g Gv .78 Gv Block Design e.BD .37 .32 .89 s.MR .59 Matrix Reasoning .79 e.MR Induction Induction .33 .48 s.PCn .64 .86 Picture Concepts Arithmetic e.PCn .64 .42 s.DS .69 .63 Digit Span e.DS .55 .51 .35 Gsm Gsm .36 .72 s.LNS .62 Letter-Number Seq. s.AR e.AR e.LNS .51 .42 s.CD .46 .29 Coding d.Gsm e.CD .39 s.SS .53 .80 Gs Symbol Search .84 e.SS .46 .54 s.CA .73 Cancellation d.Gs .50 e.CA .46

27. s.SI d.Gc Similarities s.VO Vocabulary s.CO Gc Comprehension d.Gv s.IN Information s.WR d.Ind Word Reasoning s.PCm Picture Completion s.BD g Gv Block Design s.MR Matrix Reasoning Induction s.PCn Picture Concepts Arithmetic s.DS Digit Span Gsm s.LNS Letter-Number Seq. s.AR s.CD Coding d.Gsm s.SS Gs Symbol Search s.CA Cancellation d.Gs

28. s.SI d.Gc e.Gc Similarities s.VO Vocabulary Estimated Gc s.CO Comprehension d.Gv s.IN Information s.WR d.Ind Word Reasoning s.PCm Picture Completion s.BD g Gv Block Design s.MR Matrix Reasoning Induction s.PCn Picture Concepts Arithmetic s.DS Digit Span Gsm s.LNS Letter-Number Seq. s.AR s.CD Coding d.Gsm s.SS Gs Symbol Search s.CA Cancellation d.Gs

29. s.SI d.Gc Similarities e.d.Gc s.VO Vocabulary s.CO Comprehension d.Gv s.IN Information s.WR d.Ind Word Reasoning s.PCm Picture Completion s.BD g Block Design s.MR Matrix Reasoning s.PCn Picture Concepts Arithmetic s.DS Digit Span s.LNS Letter-Number Seq. s.AR s.CD Coding d.Gsm s.SS Symbol Search s.CA Cancellation d.Gs

30. s.SI Est. d.Gc Similarities e.d.Gc s.VO Vocabulary s.CO Comprehension d.Gv s.IN Information s.WR d.Ind Word Reasoning s.PCm Picture Completion s.BD g Block Design s.MR Matrix Reasoning s.PCn Picture Concepts Arithmetic s.DS Digit Span s.LNS Letter-Number Seq. s.AR s.CD Coding d.Gsm s.SS Symbol Search s.CA Cancellation d.Gs

31. s.SI Est. d.Gc Similarities e.d.Gc s.VO Vocabulary s.CO Comprehension d.Gv s.IN Information s.WR d.Ind Word Reasoning s.PCm Picture Completion s.BD g Block Design s.MR Matrix Reasoning s.PCn Picture Concepts Arithmetic s.DS Digit Span s.LNS Letter-Number Seq. s.AR s.CD Coding d.Gsm s.SS Symbol Search s.CA Cancellation d.Gs

32. s.SI Est. d.Gc Similarities e.d.Gc s.VO Vocabulary s.CO Comprehension d.Gv s.IN Information s.WR d.Ind Word Reasoning s.PCm Picture Completion s.BD g Block Design s.MR Matrix Reasoning s.PCn Picture Concepts Arithmetic s.DS Digit Span s.LNS Letter-Number Seq. s.AR s.CD Coding d.Gsm s.SS Symbol Search s.CA Cancellation d.Gs

33. 95% CI (g) ω = 0.81 95% CI (IQ) ρxx = 0.97 WISC-IV FSIQ

34. 0.6% d.Ind d.Gv 1.8% 1.0% d.Gsm g d.Gs 2.7% 3.2% Error WISC-IV FSIQ 3.8% d.Gc 80.7% Specific 6.1%

35. 0.4% d.Ind 0.6% d.Gsm 0.4% d.Gs 1.3% d.Gv g Error 2.5% Estimated g 2.9% d.Gc 86.6% Specific 5.3%

41. I have nothing to offer but doubt, dread, fuss, and strain. You ask, what is our aim? I can answer in one word: Validity. Validity at all costs— Validity in spite of all illusions— Validity, however daunting or dreary the task may be, for without validity there is no purpose. You changed my speech!

42. The Future?

43. .71 .43 Similarities .50 .74 Vocabulary Gc .42 .63 Comprehension .39 .74 Information .42 .62 Word Reasoning .31 .11 .51 .48 Picture Completion Gv .43 .65 Block Design .26 g .67 .18 Matrix Reasoning .27* Gf .27* Picture Concepts .53 .36* Digit Span Gsm .56 .36* Letter-Number Seq. .64 .16 Coding .64 .43 Gs .22 .41 Symbol Search .54 .47 .11 Cancellation .19 Arithmetic .84

44. Predictions!

45. Spreadsheets WISC-IV WAIS-IV