Research That Matters (January 17 - 20, 2008)

The workshop will focus on the following topics.

1. Definition and illustration of time series data. In statistics, a time series is a sequence of data points, measured typically at consecutive times and spaced at equal time intervals (Wikipedia, 2007). A time series may be outcome data observed at successive times for an individual, or outcome data observed at successive times for a group of individuals (e.g., an agency or a county). A distinctive feature of such data is non-permissible of missing data at any time point. 2. The stationary assumption. Most time-series models assume a stationary process, which is a stochastic process whose probability distribution at a fixed time is the same across all time points (Wikipedia, 2007). In social work applications, this means a fixed mean and variance of time series at all times. 3. Why the method is useful in social work research? Child welfare researchers often use an individual-level approach (such as survival analysis) to analyze foster care outcomes. An aggregate-level approach using time series data can address important research questions than the individual-level analysis, simply because “individual- and aggregate-level dynamics are inseparable” (Wulzcyn, 1996). 4. Curve smoothing approaches. In order to remove random fluctuations and thereby reveal trends in the time-series data, analysts often need to conduct curve smoothing before observing trends graphically. We will present results of a comparative study of four smoothing techniques: simple moving averages, weighted moving averages, exponentially weighted moving averages, and locally weighted regression with a tricube kernel or lowess (Fox, 2000; Pindyck & Rubinfeld, 1998; SAS, 1995), and conclude that the lowess approach is the best among the four. 5. Statistical models. When modeling time series data with a limited number of units (say, n < 10), one may consider an autoregressive regression model, which assumes an error term that follows an autoregressive process with a given order of AR(p). When modeling time series data of multiple units (n > 10), one may use a growth curve analysis or HLM with either an autoregressive or an unstructured variance-covariance matrix of random effects.

We will use a real example evaluating the North Carolina's Title IV-E Waiver Demonstration program to illustrate all points listed above. The most important finding of the study is that the Waiver counties did not differ substantially from the non-waiver counties in terms of the shape of change trajectory and the rate of change; without the Waiver Demonstration, these counties could have experienced a faster increase in number of entries into placement than the non-waiver counties.