Asymptotic standard errors of the estimates of the obliquely rotated parameters by the Harris-Kaiser Case II orthoblique method are derived under the assumption of the multivariate normal distribution for observed variables. A covariance structure model for observed variables is constructed such that both unrotated and orthogonally rotated parameters are involved in the model. The asymptotic standard errors for the final oblique solution (orthoblique solution) are derived by a stepwise method. First, the asymptotic variance-covariance matrix for the estimates of the unrotated and orthogonally rotated parameters is derived. Second, the delta method is used to obtain the asymptotic variances of the estimates of the obliquely rotated parameters. Results by simulation indicate that the theoretical values of the asymptotic standard errors are close to simulated ones.
The asymptotic correlations between differently rotated solutions in exploratory factor analysis are derived. The solutions are orthogonally or obliquely rotated for unstandardized or standardized manifest variables. To obtain the asymptotic correlations between different solutions, the covariance models for manifest variables have been constructed so that two sets of solutions are involved in a single covariance structure. The asymptotic correlations can be used for the statistical test of the differences of rotated solutions. The correlation matrix between the rotated factors of the first solution and those of the second is also introduced in the models with appropriate restrictions to identify the models. The asymptotic standard errors of the estimates of the correlations between the factors in different solutions are simultaneously provided. A numerical example is presented with simulated values.
This paper discusses the acculturation of Japanese descents through the approach of exploratory data analysis. When considering acculturation, it may be common sense to consider that Sansei are more assimilated with the culture of the immigrated country than are Nisei. While observing the survey results, the question “Is this really true?” occurred to me. The point of the study is to examine, by extensive sample surveys, the hypothesis that acculturation' among generations of immigrants is of two types, namely: ‘natural acculturation’ and ‘a tendency of turning toward the Japanese way of thinking.’ This is considered to be an important point when the acculturation of a race is considered. The author deals with the degree of acculturation among generations of Japanese Americans and Japanese Brazilians, based on international comparative survey results among the host society, ethnic society and different immigrant groups consisting of several generations. The results supported the hypothesis that acculturation among generations of immigrants is of two types. Possible factors related to socio-education may also exert effects on their attitudes and values.
A marginal maximum likelihood (MML) estimation method is developed for the analysis of both categorical rating data and choice data for decision making in the context of uncertain outcomes. The proposed method fits the weighted additive models with interaction terms to the data, allowing for individual differences in weights, category boundaries, and thresholds. The present study demonstrates that the MML approach will be useful for dealing with individual differences in those variables as well as the subject points previously dealt with within the framework of multidimensional scaling. Bock and Aitkin's EM algorithm is used for the MML estimation of the proposed models.
The problem of false negatives, people who really have attitudes but refrain from expressing them, could seriously bias the analysis, but has largely been neglected. Using a survey data including a number of “DON'T KNOW” responses, this paper examined whether “DON'T KNOW” respondents had underlying attitudes. We treated these nonresponses as nonignorably missing, in the sense that “DON'T KNOW” responses are related to the answer of the question in some partially unknown way. We proposed a method to estimate parameters in a logit model when the covariates are nonignorably missing. The method simultaneously employed two generalized linear models: the proportional odds model for the response variable “Party-Support”, and the multinomial logit model for the nonresponse. We found that “Don't know” responses to the Cabinet support question depended on whether the respondents supported the Cabinet, indicating the existence of false negatives. We also found that determining which party to support was based on voters' ideology, city size and stance toward the Cabinet, even with the false negatives.