The statistical effects of the misidentification of selected stationary time series models /
| Main Author: | |
|---|---|
| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1980.
|
| Subjects: | |
| Online Access: | Link to ProQuest copy Link to OAKTrust copy ProQuest, Abstract |
| Abstract: | Time-series designs are becoming more popular in the behavioral sciences, and the interrupted-time-quasi-experiment has shown a great deal of flexibility in single-subject and group designs. However, the question of which is the most appropriate analysis of data resulting from such a design is still a controversial issue. The primary weakness of the classical approaches of ANOVA and regression is their disregard for autocorrelated observations. This weakness can result in the actual Type 1 error rates that deviate from nominal levels and stem from test statistics that are generally invalid in the presence of autocorrelation. The Box-Jenkins approach offers a family of statistical models that allow for autocorrelation to be modeled. The Box-Jenkins approach was designed primarily, however, for long series (N = 50) and for forecasting. Though this is true, this approach has been used successfully for use in modeling intervention effects. To apply ARIMA models to time-series data, the analyst must identify the ARIMA (p, d, q) parameters from the autocorrelation and partial autocorrelation functions to select the most appropriate model. Since it has been shown that these parameters can be easily misidentified in short series, the statistical effects of model misidentification must be ascertained if the Box-Jenkins approach is to be useful to the behavioral sciences, and that is the purpose of this study. The design of the study used the Monte Carlo method of distribution sampling to generate time-series with known autocorrelation and to force misidentification by applying inappropriate models to the data. Three models, AR(1), MA(1) and ARMA(1,1), were each applied to 1000 samples of each combination of four data models (AR(1), MA(1), ARMA(1,1), and white noise), series length (N = 20, 50) and effect size (0, .5). From the resulting analyses, Type I error probabilities, power, and bias in standard errors and parameter estimates were determined. When the three ARIMA models were applied correctly to the data, the actual Type I error rates were always greater than the theoretical values. Under misidentification, the Type I error rates for the models were also inflated. The only exception occurred when the AR(1) model was applied to MA(1) data, and this resulted in conservative alpha levels... |
|---|---|
| Item Description: | "Major subject: Educational Psychology." Typescript (photocopy). Vita. |
| Physical Description: | xii, 161 leaves : graphs ; 29 cm |
| Bibliography: | Includes bibliographical references (leaves 136-140). |