In this paper, maximum-likelihood estimates have been obtained for covariance matrices which have the Guttman quasi-simplex structure under each of the following null hypotheses: (a) The covariance matrix Σ, can be written asTΔT′ + Γ where Δ and Γ are both diagonal matrices with unknown elements andT is a known lower triangular matrix, and (b) the covariance matrix Σ*, is expressible asTΔ*T′ + γI where γ is an unknown scalar. The linear models from which these covariance structures arise are also stated along with the underlying assumptions. Two likelihood-ratio tests have been constructed, one each for the above null hypotheses, against the alternative hypothesis that the population covariance matrix is simply positive definite and has no particular pattern. A numerical example is provided to illustrate the test procedure. Possible applications of the proposed test are also suggested.

We propose a two-step estimator for multilevel latent class analysis (LCA) with covariates. The measurement model for observed items is estimated in its first step, and in the second step covariates are added in the model, keeping the measurement model parameters fixed. We discuss model identification, and derive an Expectation Maximization algorithm for efficient implementation of the estimator. By means of an extensive simulation study we show that (1) this approach performs similarly to existing stepwise estimators for multilevel LCA but with much reduced computing time, and (2) it yields approximately unbiased parameter estimates with a negligible loss of efficiency compared to the one-step estimator. The proposal is illustrated with a cross-national analysis of predictors of citizenship norms.

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories n it is shown that if one of the raters uses the same base rates for categories 1 and n, categories 2 and n−1, and so on, then the value of quadratically weighted kappa does not depend on the value of the center cell of the agreement table. Since the center cell reflects the exact agreement of the two raters on the middle category, this result questions the applicability of the quadratically weighted kappa to agreement studies. If one wants to report a single index of agreement for an ordinal scale, it is recommended that the linearly weighted kappa instead of the quadratically weighted kappa is used.

As a method to ascertain person and item effects in psycholinguistics, a generalized linear mixed effect model (GLMM) with crossed random effects has met limitations in handing serial dependence across persons and items. This paper presents an autoregressive GLMM with crossed random effects that accounts for variability in lag effects across persons and items. The model is shown to be applicable to intensive binary time series eye-tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses. In addition, a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects.

Throughout the colonial and postcolonial history of Bougainville (North Solomons Province from 1975 to 2005, Autonomous Region of Bougainville thereafter) people have asserted their sovereignty against the Papua New Guinea (PNG) state in many different ways, from demands for land rights to unilateral declarations of independence. In the 1970s and 1980s, Arawa Bulletin, a community-owned nonprofit magazine, bore accidental witness to many of these struggles for recognition, including a clan’s dispute over public use of its land in 1987 and the outbreak of a secessionist war in 1989. News narratives from this period apply a strategy for attribution of people’s political claims in which provincial government officials are delegated a role as co-narrators of events. In the provincial officials’ narratives, popular sovereignty has two faces—primordial and civil—which only local government can harmonize. The elite model promotes institutional reform but erases alternative modes of political consciousness.

Nonparametric tests are discussed in relation to parametric tests. A distinction is made between two types of nonparametric tests. One type leads to an exact significance level, the other to an approximate significance level. The failure to distinguish between these two types has led to confusion and error. Examples are cited.

Bootstrap and jackknife techniques are used to estimate ellipsoidal confidence regions of group stimulus points derived from INDSCAL. The validity of these estimates is assessed through Monte Carlo analysis. Asymptotic estimates of confidence regions based on a MULTISCALE solution are also evaluated. Our findings suggest that the bootstrap and jackknife techniques may be used to provide statements regarding the accuracy of the relative locations of points in space. Our findings also suggest that MULTISCALE asymptotic estimates of confidence regions based on small samples provide an optimistic view of the actual statistical reliability of the solution.

A test which allows for errors of measurement is derived for the hypothesis that all the members of a population who possess a certain skill are a sub-set of the members who possess another skill. Formulae are given for one particular case when two questions are used for each skill, and for when three questions are used for each skill. An illustrative example is given for the two-question case.

Data originally analyzed by Charles H. Goodman on the MacQuarrie Test for Mechanical Ability are subjected to the principal axes factoring method. The maximum variance was extracted with three factors. Rotation to an oblique simple structure yielded a factor pattern which satisfies the simple structure concept more adequately than the orthogonal factor matrix, thus leading to greater clarity of interpretation of the factors.

This paper establishes fundamental results for statistical analysis based on diagnostic classification models (DCMs). The results are developed at a high level of generality and are applicable to essentially all diagnostic classification models. In particular, we establish identifiability results for various modeling parameters, notably item response probabilities, attribute distribution, and Q-matrix-induced partial information structure. These results are stated under a general setting of latent class models. Through a nonparametric Bayes approach, we construct an estimator that can be shown to be consistent when the identifiability conditions are satisfied. Simulation results show that these estimators perform well under various model settings. We also apply the proposed method to a dataset from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC).

This paper presents a contribution to the sampling theory of a set of homogeneous tests which differ only in length, test length being regarded as an essential test parameter. Observed variance-covariance matrices of such measurements are taken to follow a Wishart distribution. The familiar true score-and-error concept of classical test theory is employed. Upon formulation of the basic model it is shown that in a combination of such tests forming a “total” test, the singal-to-noise ratio of the components is additive and that the inverse of the population variance-covariance matrix of the component measures has all of its off-diagonal elements equal, regardless of distributional assumptions. This fact facilitates the subsequent derivation of a statistical sampling theory, there being at most m + 1 free parameters when m is the number of component tests. In developing the theory, the cases of known and unknown test lengths are treated separately. For both cases maximum-likelihood estimators of the relevant parameters are derived. It is argued that the resulting formulas will remain reasonable even if the distributional assumptions are too narrow. Under these assumptions, however, maximum-likelihood ratio tests of the validity of the model and of hypotheses concerning reliability and standard error of measurement of the total test are given. It is shown in each case that the maximum-likelihood equations possess precisely one acceptable solution under rather natural conditions. Application of the methods can be effected without the use of a computer. Two numerical examples are appended by way of illustration.

Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.

The mathematical derivation of a test for determining the fiducial limits of, and significance of difference between, means when the samples are drawn from exponential populations is presented. The test for differences between means takes the particularly simple form of the F test (the ratio of the larger to the smaller mean) with each mean possessed of 2n degrees of freedom, n being the number of cases in the sample. Random sampling, a range of scores upwards from a lower limit of zero, and independence of means from each other are necessary assumptions for the use of the test. Examples of situations in which the test should be used are given, together with a description of the necessary computational procedures. Comparisons of the results of the application of this test with the erroneous application of the critical ratio on actual data show that rather large discrepancies exist between the two tests. Results obtained by applying tests which assume normality to exponential distributions are subject to much error.

This paper presents a way to test the difference between two X2's. The test requires evaluating the difference with respect to the Tm(x) Bessel function. Included is a table of the 5 percent and 1 percent points for the Bessel function with degrees of freedom up to 100.