Evaluating Measurement Invariance with Censored Ordinal Data: A Monte Carlo Comparison of Alternative Model Estimators and Scales of Measurement

Evaluations of measurement invariance provide essential construct validity evidence. However, the quality of such evidence is partly dependent upon the validity of the resulting statistical conclusions. The presence of Type I or Type II errors can render measurement invariance conclusions meaningless. The purpose of this study was to determine the effects of categorization and censoring on the behavior of the chi-square/likelihood ratio test statistic and two alternative fit indices (CFI and RMSEA) under the context of evaluating measurement invariance. Monte Carlo simulation was used to examine Type I error and power rates for the (a) overall test statistic/fit indices, and (b) change in test statistic/fit indices. Data were generated according to a multiple-group single-factor CFA model across 40 conditions that varied by sample size, strength of item factor loadings, and categorization thresholds. Seven different combinations of model estimators (ML, Yuan-Bentler scaled ML, and WLSMV) and specified measurement scales (continuous, censored, and categorical) were used to analyze each of the simulation conditions. As hypothesized, non-normality increased Type I error rates for the continuous scale of measurement and did not affect error rates for the categorical scale of measurement. Maximum likelihood estimation combined with a categorical scale of measurement resulted in more correct statistical conclusions than the other analysis combinations. For the continuous and censored scales of measurement, the Yuan-Bentler scaled ML resulted in more correct conclusions than normal-theory ML. The censored measurement scale did not offer any advantages over the continuous measurement scale. Comparing across fit statistics and indices, the chi-square-based test statistics were preferred over the alternative fit indices, and ΔRMSEA was preferred over ΔCFI. Results from this study should be used to inform the modeling decisions of applied researchers. However, no single analysis combination can be recommended for all situations. Therefore, it is essential that researchers consider the context and purpose of their analyses.

ENHANCEMENT OF THE FAA’s ON-LINE WILDLIFE AIRCRAFT STRIKE DATABASE WITH AN INTERACTIVE GRAPHICS CAPABILITY

Embry-Riddle Aeronautical University (Prescott, AZ, USA) was awarded a grant from the William J. Hughes FAA Technical Center in October 1999 to develop and maintain a web site dealing with a wide variety of airport safety wildlife concerns. Initially, the web site enabled users to access related topics such as wildlife management (at/near airports), bird identification information, FAA wildlife management guidelines, education, pictures, current news, upcoming meetings and training, available jobs and discussion/forum sections. In April 2001, the web site was augmented with an on-line wildlife strike report (FAA Form 5200-7). Upon submittal on-line, “quick look” email notifications are sent to concerned government personnel. The distribution of these emails varies as to whether there was damage, human injuries/fatalities, and whether feather remains were collected and will be sent to the Smithsonian Institution for identification. In July 2002, a real-time on-line query system was incorporated to allow federal and local government agencies, airport and operator personnel, and USDA and airport wildlife biologists to access this database (which as of June 2005 contains 68,288 researched strike reports added to at a rate of approximately 500 strike reports/month) to formulate strategies to reduce the hazards wildlife present to aviation. To date (June 2005), over 15,000 on-line real-time queries were processed. In June 2004, ERAU was authorized to develop a graphical interface to this on-line query system. Current capabilities include mapping strikes (by species) on the US map, each of the contiguous 48 state maps (with AK and HI being added), and airport diagrams of the major metropolitan airports as well as the next 46 airports with the most reported strikes The latter capability depicts strikes by runway in plan as well as in elevation view. Currently under development is the ability to view time-sequenced strikes on the US map. This extensive graphical interface will give analysts the ability to view strike patterns with a wide variety of variables including species, seasons, migration patterns, etc. on US and state maps and airport diagrams.