Multivariate multilevel modeling

Second, the researcher must decide whether parameter values i. Additionally, the researcher must decide whether to employ a maximum likelihood estimation or a restricted maximum likelihood estimation type. In addition, this model provides information about intraclass correlations, which are helpful in determining whether multilevel models are required in the first place. This model assumes that intercepts are fixed the same across different contexts.

Multivariate multilevel modeling

Abstract Response times on test items are easily collected in modern computerized testing. When collecting both binary responses and continuous response times on test items, it is possible to measure the accuracy and speed of test takers.

To study the relationships between these two constructs, the model is extended with a multivariate multilevel regression structure which allows the incorporation of covariates to explain the variance in speed Multivariate multilevel modeling accuracy between individuals and groups of test takers.

Model-specific implementations of a Bayes factor BF and deviance information criterium DIC for model selection are proposed which are easily calculated as byproducts of the MCMC computation. Both results from simulation studies and real-data examples are given to illustrate several novel analyses possible with this modeling framework.

Introduction Response times RTs on test items can be a valuable source of information on test takers and test items, for example, when analyzing the speededness of the test, calibrating test items, detecting cheating, and designing a test e.


With the introduction of computerized testing, their collection has become straightforward. It is important to make a distinction between the RTs on the test items and the speed at which a test taker operates throughout the test, especially when each person takes a different selection of items, as in adaptive testing.

For two different test takers, it is possible to operate at the same speed, but produce entirely different RTs because the problems formulated in their items require different amounts of information to be processed, different problem-solving strategies, etc.

Another potential confounding relationship is that between speed and accuracy. Tate was one of the first to examine the relationship between speed and accuracy on different tests.

He concluded that for a controlled level of accuracy, each test taker worked at a constant speed.

Multivariate multilevel modeling

Furthermore, test takers working at a certain speed do not necessarily demonstrate the same accuracy. Some of these findings can be explained by the well-known speed-accuracy trade-off e. The trade-off reflects the fact that speed and accuracy are main determinants of each other.

Also, they are negatively related. When a person chooses to increase his speed, then his accuracy decreases. But once his speed is fixed, his accuracy remains constant.

Observe that this trade-off involves a within-person constraint only; it does not enable us to predict the speed or accuracy of one person from another taking the same test. In order to model the relationship between speed and accuracy adequately, we therefore need a model with different levels.

Multivariate multilevel modeling

This multilevel perspective has not yet been dominant in the psychometric literature on RT modeling. However, a hierarchical framework for modeling responses and RTs was introduced in van der Linden The framework has separate first-level models for the responses and RTs.Multivariate Multilevel Models Applied Multilevel Models for Cross‐Sectional Data As an alternative approach to modeling time‐varying predictors Multivariate Multilevel Models 9 Multivariate Longitudinal Data Structure.

As such, multilevel models provide an alternative type of analysis for univariate or multivariate analysis of repeated measures.

Individual differences in growth curves may be examined. Multilevel Analysis: an Introduction to Basic and Advanced Multilevel Modeling (2nd ed.). London: Sage. Advantages of multivariate multilevel models A multivariate multilevel model is a model with multiple outcome variables. The outcome variables may or may not be longitudinal measurements of the same variable or characteristic.

Is it possible to perform a multivariate multilevel model with Stata?

The first thing to note about multivariate models is that a two-level multivariate model in reality has three levels. Like for growth models, the use of a multivariate model (as opposed to a univariate model) requires an extra level: the Intra-Individual Level.

Multivariate Multilevel Models Example • Data come from girls ages 7 through 14 that were part of a fitness training program in a southeastern state. Advantages of multivariate multilevel models A multivariate multilevel model is a model with multiple outcome variables. The outcome variables may or may not be longitudinal measurements of the same variable or.

Multivariate or Multivariable Regression?