When scientists in many fields such as educational research, psychometrics, sociology, economics, etc. are interested in knowing the values of, or inferring causal relations between variables that they cannot directly measure, they typically record several survey or test "items" that are thought to be indicators of latent variables of interest, e.g. "mathematical ability" (educational research) or personality traits such as "impulsiveness" (psychometrics). Although it is rare that a latent variable is measured perfectly by any single indicator, estimates of the latent variables, and their associations with other latents, can be obtained by employing multiple indicators for each latent variable. If the multiple indicator model is correctly specified, then in a wide range of cases the estimates obtained are consistent and have desirable statistical properties, and these estimates can be used to search for causal models among the latents. If the model is mis-specified, then estimators are typically biased, and search for causal models among the latents is more difficult. A number of problems make it difficult to find a correctly specified measurement model from background knowledge and samples of the measured variables: a) associations among items are often confounded by additional unknown latent common causes, b) there are often a plethora of alternative models that are consistent with the data and with the prior knowledge of domain experts, c) there may be non-linear dependencies among latent variables, or linear relationships among non-Gaussian latent variables, and d) there may be feedback relationships among latent variables. The investigator and his colleagues perform research that utilizes and generalizes recent work in algebraic statistics on rank constraints on sub-matrices of the measured correlation matrix that are robustly entailed by given measurement models, in order to construct reliable search algorithms that allow scientists to find correctly specified measurement models using background knowledge and sample data, and to use the measurement models to reliably construct models that specify how the latent variables are causally related to each other.
Since the early 20th century, beginning with the work of Charles Spearman on finding statistical evidence for a single trait he called "general intelligence," there has been controversy on how to scientifically determine the dimensions of personality and mental abilities; e.g. is there one dimension to intelligence ("general intelligence") or are there many different kinds of intelligence? Although there has been a great deal of progress in psychometrics, psychometric methods are still rapidly evolving. The investigators and their colleagues study how to use evidence from survey data to reliably conclude how many dimensions various personality and mental abilities have, and to construct psychological theories based on these conclusions. Potential applications include building effective educational interventions, building effective surveys for detecting personality disorders, and building effective surveys for measuring mental health in individuals and in populations.
