Latent variables in psychology and social sciences: theoretical positions, assumptions, and methodological conundrums Alina Zlati

Intelligence Attitutes Socio-economic status Self-esteem Prejudice Depression

Among the first uses of latent variables... Unobservable causes  Ra – God of sun  Thor – God of thunder  Thanatos – God of death Observable phenomena  Light, warmth, and growth  Thunder  Death

Latent variable conceptualizations  There is no single definition of the latent variables, applicable to all statistical models that make use of such variables  Rather, there are several definitions of the latent variables that vary according to the statistical model employed

Nonformal conceptualizations  Hypothetical constructs: self-esteem is not real VS  Unmeasurable constructs: self-esteem canot be directly measured VS  Data reduction devices: self-esteem is a term we assign to a factor in order to summarize a set of items that load on that factor

Formal conceptualizations – Local Independence The local independence postulate implies that all manifest variables are independent variables if the latent variables are controlled for Implications:  Errors of measurement are independent  Observed variables (indicators) have no direct or indirect effects on each other  We have at least two observed variables  Each latent variable must have direct effects on one or more observed variables  The observed variables (indicators) do not directly affect the latent variable P[Y 1,Y 2,...,Y K ]=P[Y 1 │η]P[Y 2 │η]...P[Y K │η]

Formal conceptualizations – Expected Value The latent variable (the trues score) is equal to the expected value of the observed variable for a particular individual Implications  The scale of the latent variable is defined by E(Y i )  The error of measurement has a mean of zero and is uncorrelated with T i  The errors of measurement are uncorrelated for two different observable variables  The true scores have direct effects on their corresponding observed variable  The observed variables do not directly affect the latent variable  Two different observed variables have no direct or indirect effect on each other T i ΞE(Y i )

Formal conceptualizations – Nondeterministic Function of Observed Variables A variable in a linear structural equation system is latent if the equations cannot be manipulated so as to express the variable as a function of manifest variables only Implications  This definition is devised for linear structural equations

Formal conceptualizations – Sample Realization  A latent variable is a variable for which there is no sample realization for at least some observations in a given sample

Nonformal and formal conceptualizations - Discussion

Properties  A posteriori latent variables are latent variables that a researcher derives from the data analysis  A priori latent variables are hypotehsized before the data analysis  Continuous latent variables  Categorical latent variables  Hybrid latent variables  The indicators of a latent variable are causal indicators  The indicators of a latent variable are effect indicators

Statistical models that employ latent variables  Multiple regression models  Factor analysis  Latent class analysis  Structural equation models

Statistical models that employ latent variables ModelLocal Independence Expected Value Nondeterministic Function Sample Realization Multiple Regression No Yes Factor Analysis No Yes Latent Class Analysis YesNoYes Structural Equations SometimesNoYes

Methodological conundrums „How does one know that attitudes exist at all? Only by necessary inference. There must be something to account for the consistency of conduct.” (Allport, 1935) Wicker (1969): the correlation between attitude reports and behaviors is rarely above.30, and often near zero Paulson, Lord, & Bond (2005): the relationship between attitude reports and behaviors increases to.40 when moderating variables are taken into account

Methodological conundrums  To design studies that test hypotheses about latent variables  To falsify hypotheses about latent variables  To use latent variables given the wide range of definitions  To measure latent variables

Methodological conundrums  Arbitrary metrics: not knowing where a given score locates an individual on the underlying psychological dimension or how a one-unit change on the observed score reflects the magnitude of change on the underlying dimension

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