ConstructsConstructs

AKA...AKA... Latent variablesLatent variables Unmeasured variablesUnmeasured variables FactorsFactors Unobserved variablesUnobserved variables True scoresTrue scores

ConstructsConstructs

What is a construct?What is a construct? Constructs become better defined via Constructs become better defined via

researchresearch Temperature, pH, bacteria, gas pressure, Temperature, pH, bacteria, gas pressure,

electricityelectricity 1. An unobserved 1. An unobserved causecause of variation of variation

in an observable variable(s)in an observable variable(s) 2. A label used to describe a pattern 2. A label used to describe a pattern

of observed covariancesof observed covariances

Basic Measurement ModelBasic Measurement Model

Construct

Measure 1 Measure 2 Measure 3

Error 1 Error 2 Error 3

Perspectives on ConstructsPerspectives on Constructs

Bollen (2002) ...Bollen (2002) ...

Perspectives on ConstructsPerspectives on Constructs

Informal PerspectivesInformal Perspectives Platonic viewPlatonic view

Constructs are real – Loevinger (1957)Constructs are real – Loevinger (1957) Social construction or construalSocial construction or construal

A theory or model - Nunnally (1978)A theory or model - Nunnally (1978) Unmeasurable variablesUnmeasurable variables

Only indirect proxies are possible – Joreskog Only indirect proxies are possible – Joreskog (1979)(1979)

Data reductionData reduction Summary of the relations among a number of Summary of the relations among a number of

variables – Harmon (1960)variables – Harmon (1960)

Perspectives on ConstructsPerspectives on Constructs

Local Independence perspectiveLocal Independence perspective Latent variable is responsible for or Latent variable is responsible for or

causes covariation in observed causes covariation in observed manifestationsmanifestations

If you control for the latent variable, the If you control for the latent variable, the observed manifestations would be observed manifestations would be uncorrelated.uncorrelated.

Assumes that the manifestations are only Assumes that the manifestations are only caused by the construct and no other caused by the construct and no other constructsconstructs

UnidimensionalityUnidimensionality

Basic assumption for item response Basic assumption for item response theory - theory -

Lord (1953); Lazarsfeld (1959)Lord (1953); Lazarsfeld (1959)

Perspectives on ConstructsPerspectives on Constructs

Expected Value perspectiveExpected Value perspective Associated with classical test theoryAssociated with classical test theory True scoreTrue score A person's true score is the expected A person's true score is the expected

value (mean) of a distribution of scores value (mean) of a distribution of scores obtained via the replication or repeated obtained via the replication or repeated measurement within the individual measurement within the individual

Lord & Novick (1968)Lord & Novick (1968)

Perspectives on ConstructsPerspectives on Constructs

Nondeterministic function of observed Nondeterministic function of observed variablesvariables the latent variable is not completely the latent variable is not completely

determined by the observed variablesdetermined by the observed variables Bentler (1982)Bentler (1982)

Can estimate or predict a value for the Can estimate or predict a value for the construct but can't compute it directlyconstruct but can't compute it directly

Perspectives on ConstructsPerspectives on Constructs

Sample Realizations - Bollen's Sample Realizations - Bollen's perspectiveperspective A latent random variable is a random A latent random variable is a random

variable for which there is no sample variable for which there is no sample realization for at least some of the realization for at least some of the observations in a given sampleobservations in a given sample

Analogous to missing valuesAnalogous to missing values All variables are latent until sample All variables are latent until sample

values of them are obtainedvalues of them are obtained Sample dependent definitionSample dependent definition Instrument dependent – error in Instrument dependent – error in

temperaturetemperature

Perspectives on ConstructsPerspectives on Constructs

Random variables vs. constructsRandom variables vs. constructs e.g., residuals in regressione.g., residuals in regression HLM models with random intercepts or HLM models with random intercepts or

slopesslopes

Causality and MeasurementCausality and Measurement

Scientist and theorist don't always Scientist and theorist don't always agree...agree...

Measurement requires causal Measurement requires causal inferenceinference Changes in the level of the latent entity Changes in the level of the latent entity

cause changes in the level of the cause changes in the level of the indicator variable(s).indicator variable(s).

This inference requires the same This inference requires the same scientific method as any causal research scientific method as any causal research question.question.

Must show that the latent variable is the Must show that the latent variable is the only cause of the indicator (construct only cause of the indicator (construct validity)validity)

Model of MeasurementModel of Measurement

Construct

Construct = an unobservable but real causal variable(aka latent variable)

Indicator / Instrument

Indicator = an observable variable thatis solely caused by the construct andsensitive to changes in the level of the construct

Scale: the rule for assigning numbers to the levels of theindicator or instrument

A bit more complex...A bit more complex...

Continuum (X~)

Construct (Xc)

Measure (Xm)

Xm = f(X~)

Continuum (Y~)

Construct (Yc)

Measure (Ym)

Ym = f(Y~)

Ym = f(Xm)

Some quotes to think aboutSome quotes to think about

"I often say that when you can measure what you are "I often say that when you can measure what you are speaking about, and express it in numbers, you know speaking about, and express it in numbers, you know something about it; but when you cannot measure it, something about it; but when you cannot measure it, when you cannot express it in numbers, your when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.“ Sir William science, whatever the matter may be.“ Sir William Thomson, Lord Kelvin. 1889 Thomson, Lord Kelvin. 1889

““Whatever exists at all, exists in some amount. To Whatever exists at all, exists in some amount. To know it thoroughly involves knowing its quality as know it thoroughly involves knowing its quality as well as its quantity” Thorndike, 1918well as its quantity” Thorndike, 1918