From a methodological perspective, I have three principle research interests: (1) continuous and categorical
dynamic factor models and nonlinear time series models, (2) linear and nonlinear models for analyzing longitudinal
data, and (3) Bayesian estimation methods and statistical computing. From a substantive perspective, I am
interested in the analysis of intraindividual change and interindividual differences in change in life span
development, cognitive aging, and emotion.
With the growing emphasis on analyzing change through modeling systematic fluctuation and patterns of
intraindividual variability, collecting time series data is expected to become a more regular routine in behavioral
science. Although the traditional time series analytic techniques such as ARMA, ARIMA, and VARMA models can
be used in simple conditions, complex models such as P-technique factor models and dynamic factor models
are desired for psychologica research involving multivariate response data and latent constructs. My research
has involved continuous and categorical dynamic factor models and nonlinear time series models.
In one study, we reviewed three previous methods: Kalman filter method, least squares method and maximum
likelihood method, and proposed a new Bayesian method using Gibbs sampling for estimating a dynamic factor
model (Zhang, Hamaker, & Nesselroade, in press). We concluded that all four methods can reach appropriate
parameter estimates with comparable precision. We implemented all four estimation procedures in currently
available software and have made the program codes available to researchers. They provide researchers useful
tools to carry out dynamic factor analysis of continuous time series data.
In another study, we extended two main dynamic factor model variations - the direc autoregressive factor score
(DAFS) model and the white noise factor score (WNFS) model - to the categorical DAFS and WNFS models in
the framework of the underlying variable method (Zhang & Nesselroade, in press). Based on the analysis of both
simulated data and empirical data from an emotion study, we concluded that categorical dynamic factor models
were more appropriate when analyzing categorical time series data.
In the third study (Hamaker, Zhang, & van der Maas, under revision), we investigated the nonlinear time series
analysis of dynamic systems. We put the "equations of marriage" in the more general threshold autoregressive
model framework and presented a new estimation procedure for Gottman's interaction models. We concluded
that the new method produced les biased, more efficient parameter estimates. This method is especially useful
for bivariate systems such as dyadic interactions and opens the possibility for examining interactions of more
complex systems.
Growth curve models are one of the most popular and important techniques for analyzing longitudinal data to
explore intraindividual change and interindividual differences in change. These models have been widely used in
multiple disciplines, such as psychology, gerontology, biology, and health research. I have contributed to the
development of growth curve techniques in several ways.
First, we extended growth curve models to include prior research findings in current research to articulate the
power of cumulation of knowledge (Zhang, Hamagami, Wang, Grimm, & Nesselroade, 2007). After showing that
Bayesian estimation with non-informative priors can obtain the same results as the maximum estimation method,
we incorporated the available prior information into growth curve analysis through informative prior distributions.
We concluded that using prior information can improve statistical efficiency and power. This technique has a
promising future for analyzing data with small sample size or nonnormally distributed variables.
Second, we extended growth curve models to deal with longitudinal ceiling data (Wang, Zhang, McArdle, &
Salthouse, under review). After showing that ceiling effects may lead to serious artifactual findings in
longitudinal analysis, we investigated several methods of dealing with ceiling effects through Monte Carlo
simulations and empirical data analyses. We concluded that the hierarchical Tobit model, which can be viewed
as an extension of growth curve models, was a robust way to deal with ceiling problems. This method is also
useful for dealing with floor effects.
Third, in my dissertation research, I am extending growth curve models to analyze both level of growth and rate
of growth (change) simultaneously. The rate of growth represents the dynamic feature of a growth process.
However, current growth curve models are limited to analyzing rate of growth in linear growth curve models
directly and quadratic growth curve models indirectly. To analyze the rate of growth with a stronger, more
versatile approach, I am developing a series of growth rate models, univariate or multivariate, linear or nonlinear,
by defining the rate of growth using both parametric and non-parametric methods. Growth rate models can help
researchers understand growth processes more fully than is currently the case.
Bayesian methods have played a very important role in my research, in part, because I believe they have an
important role to play in the future of behavioral science. I have applied Bayesian methods to estimating a
variety of models, such as dynamic factor models (Zhang, Hamaker, & Nesselroade, in press; Zhang &
Nesselroade, in press), growth curve models (Wang et al., under review; Zhang, Hamagami, et al., 2007),
growth rate models (Zhang, 2008), and latent difference score models (Hamagami, Zhang, & McArdle, in
preparation). Gibbs sampling and other Markov chain Monte Carlo methods were used in Bayesian estimation methods.
I believe that Bayesian methods have a promising future in psychological research, especially in quantitative
model development. I have worked on two projects to develop SAS macros and stand-alone software to
facilitate the adoption and application of Bayesian methods.
In one project, we presented a SAS Interface on how to implement Bayesian analysis with WinBUGS - a widely
used Bayesian analysis program - as part of a standard set of SAS routin (Zhang, McArdle, Wang, & Hamagami,
in press). Using the multiple regression model, the growth curve model, and the factor model, we illustrated how
to implement Bayesian analysis inside SAS for both single data set analysis and Monte Carlo simulation studies.
This interface can be of practical benefit in many aspects of Bayesian methods because it allows SAS users to
benefit from the implementation of Bayesian estimation and it also allows WinBUGS users to benefit from the
data processing routines available in SAS.
In another project, we developed a program called BAUW (Bayesian Analysis using WinBUGS, Zhang & Wang,
2006). We provided BAUW as free software which can convert data to compatibility with WinBUGS and generate
WinBUGS codes for many kinds of models, such as regression models, growth curve models, and IRT models.
BAUW largely eases the use of WinBUGS and we expect that it will advance the use of Bayesian methods in
psychology.
The bootstrap technique is becoming increasingly popular in psychological research because it has no
distribution assumption on parameter estimates. Combined with least squares estimation methods, it is more
appropriate for analyzing small sample size or non-normal data than maximum likelihood estimation methods.
We have investigated how to evaluate mediation effects for small sample size and heterogeneity data using
bootstrap methods (Zhang & Wang, in preparation). The three different methods in this study can be
implemented conveniently in the software provided (Zhang & Wang, 2007b). We concluded that bootstrap
methods should be used in mediation analysis when the sample size is small or the data are heteroscedastic.
Highly influenced by Dr. John Nesselroade and Dr. Timothy Salthouse, I have developed my substantive
interests in the analysis of intraindividual change and interindividual differences in change in life span
development, cognitive aging, and emotion.
In one study, we investigated intraindividual change and interindividual differences in short-term verbal and
spatial learning and their relationship with age, fluid intelligence and crystallized intelligence (Zhang, Davis,
Salthouse, & Tucker-Drob, 2007). Based on multiple group and multivariate growth curve analysis, we
concluded that individual differences in learning do exist and people vary with respect to efficiency of learning.
However, we did not find the existence of a general learning ability.
In another study, we investigated whether training can prevent the loss of learning ability using the data from
the Advanced Cognitive Training for Independence and Vital Elderly study (Zhang, Wang, & Hamagami, 2006).
A second-order growth curve model was used to separate agin effects from training effects. We found that a
negative but artificial training effect was present without considering age effects in an aging study. After
accounting for age effects, memory training was found to prevent long term loss of short term learning abilit.
In an ongoing study we are investigating whether cognitive training interventions improve cognitive abilities and
daily functioning in older, independent-living adults both in short term and long term. Based on longitudinal
mediation models with autoregressive structures, we calculate and predict the dynamic changes of training
effects on daily functioning with age. We find that training effects peaked after 6 years of initial training and
could last more than 25 years with booster training. This study will be presented in the upcoming meeting of
the Gerontological Society of America (Zhang & Wang, 2007a).