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Distance sampling is one of the most commonly used methods for estimating density and abundance. Conventional methods are based on the distances of detected animals from the center of point transects or the center line of line transects. These distances are used to model a detection function: the probability of detecting an animal, given its distance from the line or point. The probability of detecting an animal in the covered area is given by the mean value of the detection function with respect to the available distances to be detected. Given this probability, a Horvitz-Thompson- like estimator of abundance for the covered area follows, hence using a model-based framework. Inferences for the wider survey region are justified using the survey design. Conventional distance sampling methods are based on a set of assumptions. In this thesis I present results that extend distance sampling on two fronts. Firstly, estimators are derived for situations in which there is measurement error in the distances. These estimators use information about the measurement error in two ways: (1) a biased estimator based on the contaminated distances is multiplied by an appropriate correction factor, which is a function of the errors (PDF approach), and (2) cast into a likelihood framework that allows parameter estimation in the presence of measurement error (likelihood approach). Secondly, methods are developed that relax the conventional assumption that the distribution of animals is independent of distance from the lines or points (usually guaranteed by appropriate survey design). In particular, the new methods deal with the case where animal density gradients are caused by the use of non-random sampler allocation, for example transects placed along linear features such as roads or streams. This is dealt with separately for line and point transects, and at a later stage an approach for combining the two is presented. A considerable number of simulations and example analysis illustrate the performance of the proposed methods.

Social science researchers are increasingly using multi-group confirmatory factor analysis (MG-CFA) to compare different groups' latent variable means. To ensure that a MG-CFA model is identified, two approaches are commonly used to set the scale of the latent variable. The reference indicator (RI) strategy, which involves constraining one loading per factor to a value of one across groups, assumes that the RI has equal factor loadings across groups. The second approach involves constraining each factor's variance to a value of one across groups and, thus, assumes that the factor variances are equal across groups. Latent mean differences may be tested and described using Gonzalez and Griffin's (2001) likelihood ratio test (LRT[subscript k]) and Hancock's (2001) standardized latent mean difference effect size measure ([delta subscript k]), respectively. Applied researchers using the LRT[subscript k] and/or the [delta subscript k] when comparing groups' latent means may not explicitly test the assumptions underlying the two factor scaling methods. To date, no study has examined the impact of violating the assumptions associated with the two scaling methods on latent mean comparisons. The purpose of this study was to assess the performance of the LRT[subscript k] and the [delta subscript k] when violating the assumptions underlying the RI strategy and/or the factor variance scaling method. Type I error and power of the LRT[subscript k] as well as relative parameter bias and parameter bias of the [delta subscript k] were examined when varying loading difference magnitude, factor variance ratio, factor loading pattern and sample size ratio. Rejection rates of model fit indices, including the x² test, RMSEA, CFI, TLI and SRMR, under these varied conditions were also examined. The results indicated that violating the assumptions underlying the RI strategy did not affect the LRT[subscript k] or the [delta subscript k]. However, violating the assumption underlying the factorvariance scaling method influenced Type I error rates of the LRT[subscript k], particularly in unequal sample size conditions. Results also indicated that the four factors manipulated in this study had an impact on correct model rejection rates of the model fit indices. It is hoped that this study provides useful information to researchers concerning the use of the LRT[subscript k] and [delta subscript k] under factor scaling method assumption violations. / text