A New Birth-Interval Approach to Estimating Demographic Parameters of Humpback Whales

A demographic model is developed based on interbirth intervals and is applied to estimate the population growth rate of humpback whales (Megaptera novaeangliae) in the Gulf of Maine. Fecundity rates in this model are based on the probabilities of giving birth at time t after a previous birth and on the probabilities of giving birth first at age x. Maximum likelihood methods are used to estimate these probabilities using sighting data collected for individually identified whales. Female survival rates are estimated from these same sighting data using a modified Jolly–Seber method. The youngest age at first parturition is 5 yr, the estimated mean birth interval is 2.38 yr (SE = 0.10 yr), the estimated noncalf survival rate is 0.960 (SE = 0.008), and the estimated calf survival rate is 0.875 (SE = 0.047). The population growth rate (l) is estimated to be 1.065; its standard error is estimated as 0.012 using a Monte Carlo approach, which simulated sampling from a hypothetical population of whales. The simulation is also used to investigate the bias in estimating birth intervals by previous methods. The approach developed here is applicable to studies of other populations for which individual interbirth intervals can be measured.

Improving IRT parameter estimates with small sample sizes: Evaluating the efficacy of a new data augmentation technique

The 3PL model is a flexible and widely used tool in assessment. However, it suffers from limitations due to its need for large sample sizes. This study introduces and evaluates the efficacy of a new sample size augmentation technique called Duplicate, Erase, and Replace (DupER) Augmentation through a simulation study. Data are augmented using several variations of DupER Augmentation (based on different imputation methodologies, deletion rates, and duplication rates), analyzed in BILOG-MG 3, and results are compared to those obtained from analyzing the raw data. Additional manipulated variables include test length and sample size. Estimates are compared using seven different evaluative criteria. Results are mixed and inconclusive. DupER augmented data tend to result in larger root mean squared errors (RMSEs) and lower correlations between estimates and parameters for both item and ability parameters. However, some DupER variations produce estimates that are much less biased than those obtained from the raw data alone. For one DupER variation, it was found that DupER produced better results for low-ability simulees and worse results for those with high abilities. Findings, limitations, and recommendations for future studies are discussed. Specific recommendations for future studies include the application of Duper Augmentation (1) to empirical data, (2) with additional IRT models, and (3) the analysis of the efficacy of the procedure for different item and ability parameter distributions.