Psychometricians make use of a very wide range of statistical models, for example:

Regression analysis
Path analysis
Exploratory factor analysis
Confirmatory factor analysis
Item response theory modeling
Structural equation modeling
Growth modeling
Discrete-time survival analysis
Continuous-time survival analysis
Time series analysis

Observed outcome variables may be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types.

Some variations of these basic models are:

Regression mixture modeling
Path analysis mixture modeling
Latent class analysis
Latent class analysis with covariates and direct effects
Confirmatory latent class analysis
Latent class analysis with multiple categorical latent variables
Loglinear modeling
Multiple group analysis
Multilevel modeling
Finite mixture modeling
Complier Average Causal Effect (CACE) modeling
Latent transition analysis and hidden Markov modeling including mixtures and covariates
Latent class growth analysis
Discrete-time survival mixture analysis
Continuous-time survival mixture analysis

Over the years, I've used many of these models in my marketing-related work. They all have practical applications in many fields - it ain't just academic stuff.

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