1. Constructs AKA... AKA... Latent variables Latent variables Unmeasured variables Unmeasured variables Factors Factors Unobserved variables Unobserved variables True scores True scores

2. Constructs What is a construct? What is a construct? Constructs become better defined via research Constructs become better defined via research Temperature, pH, bacteria, gas pressure, electricity Temperature, pH, bacteria, gas pressure, electricity 1. An unobserved cause of variation in an observable variable(s) 1. An unobserved cause of variation in an observable variable(s) 2. A label used to describe a pattern of observed covariances 2. A label used to describe a pattern of observed covariances

3. Basic Measurement Model Construct Measure 1 Measure 2 Measure 3 Error 1Error 2Error 3

4. Perspectives on Constructs Bollen (2002)... Bollen (2002)...

5. Perspectives on Constructs Informal Perspectives Informal Perspectives Platonic view Platonic view Constructs are real – Loevinger (1957) Constructs are real – Loevinger (1957) Social construction or construal Social construction or construal A theory or model - Nunnally (1978) A theory or model - Nunnally (1978) Unmeasurable variables Unmeasurable variables Only indirect proxies are possible – Joreskog (1979) Only indirect proxies are possible – Joreskog (1979) Data reduction Data reduction Summary of the relations among a number of variables – Harmon (1960) Summary of the relations among a number of variables – Harmon (1960)

6. Perspectives on Constructs Local Independence perspective Local Independence perspective Latent variable is responsible for or causes covariation in observed manifestations Latent variable is responsible for or causes covariation in observed manifestations If you control for the latent variable, the observed manifestations would be uncorrelated. If you control for the latent variable, the observed manifestations would be uncorrelated. Assumes that the manifestations are only caused by the construct and no other constructs Assumes that the manifestations are only caused by the construct and no other constructs Unidimensionality Unidimensionality Basic assumption for item response theory - Basic assumption for item response theory - Lord (1953); Lazarsfeld (1959) Lord (1953); Lazarsfeld (1959)

7. Perspectives on Constructs Expected Value perspective Expected Value perspective Associated with classical test theory Associated with classical test theory True score True score A person's true score is the expected value (mean) of a distribution of scores obtained via the replication or repeated measurement within the individual A person's true score is the expected value (mean) of a distribution of scores obtained via the replication or repeated measurement within the individual Lord & Novick (1968) Lord & Novick (1968)

8. Perspectives on Constructs Nondeterministic function of observed variables Nondeterministic function of observed variables the latent variable is not completely determined by the observed variables the latent variable is not completely determined by the observed variables Bentler (1982) Bentler (1982) Can estimate or predict a value for the construct but can't compute it directly Can estimate or predict a value for the construct but can't compute it directly

9. Perspectives on Constructs Sample Realizations - Bollen's perspective Sample Realizations - Bollen's perspective A latent random variable is a random variable for which there is no sample realization for at least some of the observations in a given sample A latent random variable is a random variable for which there is no sample realization for at least some of the observations in a given sample Analogous to missing values Analogous to missing values All variables are latent until sample values of them are obtained All variables are latent until sample values of them are obtained Sample dependent definition Sample dependent definition Instrument dependent – error in temperature Instrument dependent – error in temperature

10. Perspectives on Constructs Random variables vs. constructs Random variables vs. constructs e.g., residuals in regression e.g., residuals in regression HLM models with random intercepts or slopes HLM models with random intercepts or slopes

11. Causality and Measurement Scientist and theorist don't always agree... Scientist and theorist don't always agree... Measurement requires causal inference Measurement requires causal inference Changes in the level of the latent entity cause changes in the level of the indicator variable(s). Changes in the level of the latent entity cause changes in the level of the indicator variable(s). This inference requires the same scientific method as any causal research question. This inference requires the same scientific method as any causal research question. Must show that the latent variable is the only cause of the indicator (construct validity) Must show that the latent variable is the only cause of the indicator (construct validity)

12. Model of Measurement Construct Construct = an unobservable but real causal variable (aka latent variable) Indicator / Instrument Indicator = an observable variable that is solely caused by the construct and sensitive to changes in the level of the construct Scale: the rule for assigning numbers to the levels of the indicator or instrument

13. A bit more complex... Continuum (X ~ ) Construct (X c ) Measure (X m ) X m = f(X ~ ) Continuum (Y ~ ) Construct (Y c ) Measure (Y m ) Y m = f(Y ~ ) Y m = f(X m )

14. Some quotes to think about "I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.“ Sir William Thomson, Lord Kelvin. 1889 "I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.“ Sir William Thomson, Lord Kelvin. 1889 “Whatever exists at all, exists in some amount. To know it thoroughly involves knowing its quality as well as its quantity” Thorndike, 1918 “Whatever exists at all, exists in some amount. To know it thoroughly involves knowing its quality as well as its quantity” Thorndike, 1918