How Good are Our Measures? Investigating the Appropriate Use of Factor Analysis for Survey Instruments

Background: Evaluation work frequently utilizes factor analysis to establish the dimensionality, reliability, and stability of surveys. However, survey data is typically ordinal, violating the assumptions of most statistical methods, and thus is often factor-analyzed inappropriately. Purpose: This study illustrates the salient analytical decisions for factor-analyzing ordinal survey data appropriately and demonstrates the repercussions of inappropriate analyses. Setting: The data used for this study are drawn from an evaluation of the efficacy of a drama-based approach to teaching Shakespeare in elementary and middle school.  Intervention: Not applicable. Research Design: Survey research. Data Collection and Analysis: Four factor analytic methods were compared: a traditional exploratory factor analysis (EFA), a full-information EFA, and two EFAs within the confirmatory factor analysis framework (E/CFA) conducted according to the Jöreskog method and the Gugiu method. Findings: Methods appropriate for ordinal data produce better models, the E/CFAs outperform the EFAs, and the Gugiu method demonstrates greater model interpretability and stability than the Jöreskog method. These results suggest that the Gugiu E/CFA may be the preferable factor analytic method for use with ordinal data. Practical applications of these findings are discussed. Keywords: factor analysis; ordinal data; E/CFA; survey research

Ordinal proof theory of Kripke-Platek set theory augmented by strong reflection principles

Diese Arbeit umfasst vier Teile. Im ersten Teil wird eine Ordinalzahlanalyse der Kripke-Platek Mengenlehre, erweitert um ein Reflexionsschema für erststufige Formeln, erarbeitet. Im zweiten Teil wird diese Ordinalzahlanalyse genutzt, um mit Hilfe subrekursiver Hierarchien eine Charakterisierung der beweisbar rekursiven Funktionen der im ersten Teil untersuchten Theorie zu erhalten. In den letzten beiden Teilen werden die in den ersten beiden Teilen entwickelten Techniken erweitert, um eine Ordinalzahlanalyse, bzw. eine Charakterisierung der beweisbar rekursiven Funktionen, der von M. Rathjen eingeführten Theorie Stabilität zu erhalten. Die Theorie Stabilität umfasst die Theorie KPi, erweitert um das Axiom: zu jeder Ordinalzahl alpha existiert eine Ordinalzahl kappa, so dass kappa kappa+alpha stabil ist. This thesis is divided into four parts. In the first part an ordinal analysis of Kripke-Platek set theory augmented by a first order reflection scheme is given. In the second part a characterization of the provable recursive functions of the above mentioned theory is acquired. These functions are characterized in terms of a subrecursive hierarchy, which is defined by means of the proof-theoretic ordinal established in the first part of this thesis. In the third part the ordinal analysis of the first part is extended to an ordinal analysis of the theory Stability. The theory Stability was introduced by M. Rathjen and denotes the axiom system of KPi augmented by the axiom: for every ordinal alpha there exists an ordinal kappa, such that kappa is kappa+alpha stable. In the last part of this thesis a characterization of the provable recursive functions of Stability is given by an application of the results of the second part to the ordinal analysis of the third part

Sparse Regression with Multi-type Regularized Feature Modeling

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such as Lasso regression for (continuous) predictors treated as linear effects. However, many predictive problems involve different types of predictors and require a tailored regularization term. We propose a multi-type Lasso penalty that acts on the objective function as a sum of subpenalties, one for each type of predictor. As such, we allow for predictor selection and level fusion within a predictor in a data-driven way, simultaneous with the parameter estimation process. We develop a new estimation strategy for convex predictive models with this multi-type penalty. Using the theory of proximal operators, our estimation procedure is computationally efficient, partitioning the overall optimization problem into easier to solve subproblems, specific for each predictor type and its associated penalty. Earlier research applies approximations to non-differentiable penalties to solve the optimization problem. The proposed SMuRF algorithm removes the need for approximations and achieves a higher accuracy and computational efficiency. This is demonstrated with an extensive simulation study and the analysis of a case-study on insurance pricing analytics

Investigating the monetary policy of central banks with assessment indicators : [Version December 2009]

This paper outlines a new method for using qualitative information to analyze the monetary policy strategy of central banks. Quantitative assessment indicators that are extracted from a central bank's public statements via the balance statistic approach are employed to estimate a Taylor-type rule. This procedure allows to directly capture a policymaker's assessments of macroeconomic variables that are relevant for its decision making process. As an application of the proposed method the monetary policy of the Bundesbank is re-investigated with a new dataset. One distinctive feature of the Bundesbank's strategy consisted of targeting growth in monetary aggregates. The analysis using the proposed method provides evidence that the Bundesbank indeed took into consideration monetary aggregates but also real economic activity and inflation developments in its monetary policy strategy since 1975. JEL Classification: E52, E58, N14 Keywords: Monetary Policy Rule, Statement Indicators, Bundesbank, Monetary Targetin