Pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variables

Correlated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on `trust in the police' selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan

The Effect of Probing "Don't Know" Responses on Measurement Quality and Nonresponse in Surveys

In survey interviews, “Don’t know” (DK) responses are commonly treated as missing data. One way to reduce the rate of such responses is to probe initial DK answers with a follow-up question designed to encourage respondents to give substantive, non- DK responses. However, such probing can also reduce data quality by introducing additional or differential measurement error. We propose a latent variable model for analyzing the effects of probing on responses to survey questions. The model makes it possible to separate measurement effects of probing from true differences between respondents who do and do not require probing. We analyze new data from an exper- iment which compared responses to two multi-item batteries of questions with and without probing. In this study, probing reduced the rate of DK responses by around a half. However, it also had substantial measurement effects, in that probed answers were often weaker measures of constructs of interest than were unprobed answers. These effects were larger for questions on attitudes than for pseudo-knowledge ques- tions on perceptions of external facts. The results provide evidence against the use of probing of “Don’t know” responses, at least for the kinds of items and respondents considered in this study

On the Radiative Corrections to the Pseudo-scalar Higgs Boson Mass

We reexamine the one-loop corrections to the mass of the pseudo-scalar Higgs boson, using the effective potential. In the absence of the chargino and neutralino contributions its mass exhibits a large scale dependence in the large $M_{1/2}$ regime, especially for values of $\tan \beta>20$. Thus, although of electroweak origin, the heaviness of the $M_{1/2}$, in conjunction with the largeness of $\tan \beta$, makes these corrections very important for establishing a scale independent result and an unambiguous determination of the pseudo-scalar mass in this region of the parameter space

Collective treatment of High Energy Thresholds in SUSY - GUTs

Supersymmetric GUTs are the most natural extension of the Standard model unifying electroweak and strong forces. Despite their indubitable virtues, among these the gauge coupling unification and the quantization of the electric charge, one of their shortcomings is the large number of parameters used to describe the high energy thresholds (HET), which are hard to handle. We present a new method according to which the effects of the HET, in any GUT model, can be described by fewer parameters that are randomly produced from the original set of the parameters of the model. In this way, regions favoured by the experimental data are easier to locate, avoiding a detailed and time consuming exploration of the parameter space, which is multidimensional even in the most economic unifying schemes. To check the efficiency of this method, we directly apply it to a SUSY SO(10) GUT model in which the doublet-triplet splitting is realized through the Dimopoulos-Wilczek mechanism. We show that the demand of gauge coupling unification, in conjunction with precision data, locates regions of the parameter space in which values of the strong coupling \astrong are within the experimental limits, along with a suppressed nucleon decay, mediated by a higgsino driven dimension five operators, yielding lifetimes that are comfortably above the current experimental bounds. These regions open up for values of the SUSY breaking parameters m_0, M_1/2 < 1 TeV being therefore accessible to LHC.Comment: 21 pages, 8 figures, UA-NPPS/BSM-10/02 (added

SOFTSUSY: a program for calculating supersymmetric spectra

SOFTSUSY is a program which accurately calculates the spectrum of superparticles in the CP-conserving Minimal Supersymmetric Standard Model (MSSM), with a full flavour mixing structure. The program solves the renormalisation group equations with theoretical constraints on soft supersymmetry breaking terms provided by the user. Weak-scale gauge coupling and fermion mass data (including one-loop finite MSSM corrections) are used as a boundary condition, as well as successful radiative electroweak symmetry breaking. The program can also calculate a measure of fine-tuning. The program structure has been designed to easily generalise to extensions of the MSSM. This article serves as a self-contained guide to prospective users, and indicates the conventions and approximations used.Comment: Updated for SOFTSUSY3.3.3. Can be downloaded from http://projects.hepforge.org/softsusy/ Further updated versions of the manual will be distributed with the cod

WMAPing out Supersymmetric Dark Matter and Phenomenology

The recent WMAP data provide a rather restricted range of the Cold Dark Matter (CDM) density $\Omega_{CDM} h^2$ of unprecedented accuracy. We combine these new data along with data from BNL E821 experiment measuring ${(g_{\mu}-2)}$, $$the {b\goes s \gamma} branching ratio and the light Higgs boson mass bound from LEP, to update our analysis of the allowed boundaries in the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM). The prospects of measuring Supersymmetry at LHC look like a very safe bet, and the potential of discovering SUSY particles at a $\sqrt{s} = 1.1 \mathrm{TeV}$ linear collider is enhanced considerably. The implications for Dark Matter direct searches are also discussed.Comment: 12 pages LaTeX, 5 eps figures included, references adde

On the Higgs Mass in the CMSSM

We estimate the mass of the lightest neutral Higgs boson h in the minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses (CMSSM), subject to the available accelerator and astrophysical constraints. For m_t = 174.3 GeV, we find that 114 GeV < m_h < 127 GeV and a peak in the tan beta distribution simeq 55. We observe two distinct peaks in the distribution of m_h values, corresponding to two different regions of the CMSSM parameter space. Values of m_h < 119 GeV correspond to small values of the gaugino mass m_{1/2} and the soft trilinear supersymmetry-breaking parameter A_0, lying along coannihilation strips, and most of the allowed parameter sets are consistent with a supersymmetric interpretation of the possibly discrepancy in g_mu - 2. On the other hand, values of m_h > 119 GeV may correspond to much larger values of m_{1/2} and A_0, lying in rapid-annihilation funnels. The favoured ranges of m_h vary with m_t, the two peaks being more clearly separated for m_t = 178 GeV and merging for m_t = 172.7 GeV. If the g_mu - 2 constraint is imposed, the mode of the m_h distribution is quite stable, being sim 117 GeV for all the studied values of m_t.Comment: 14 pages, 12 figure

On the Interpretation of B_s to mu^+ mu^- in the CMSSM

We discuss the interpretation of present and possible future experimental constraints on B_s to mu^+ mu^- decay in the context of the constrained minimal extension of the Standard Model (CMSSM) with universal scalar masses. We emphasize the importance of including theoretical and other experimental uncertainties in calculating the likelihood function, which can affect significantly the inferred 95% confidence-level limit on the CMSSM parameters. The principal uncertainties are the B_s meson decay constant, m_t and m_b. The latter induce uncertainties in the mass of the charged Higgs boson that dominates the B_s to mu^+ mu^- decay amplitude at large tan beta, reducing the CMSSM region excluded by present and possible future limits from the Fermilab Tevatron collider and the LHC.Comment: 19 pages, 12 eps figures, as appears in Phys. Lett.

Composite Likelihood Estimation for Latent Variable Models with Ordinal and Continuous, or Ranking Variables

The estimation of latent variable models with ordinal and continuous, or ranking variables is the research focus of this thesis. The existing estimation methods are discussed and a composite likelihood approach is developed. The main advantages of the new method are its low computational complexity which remains unchanged regardless of the model size, and that it yields an asymptotically unbiased, consistent, and normally distributed estimator. The thesis consists of four papers. The first one investigates the two main formulations of the unrestricted Thurstonian model for ranking data along with the corresponding identification constraints. It is found that the extra identifications constraints required in one of them lead to unreliable estimates unless the constraints coincide with the true values of the fixed parameters. In the second paper, a pairwise likelihood (PL) estimation is developed for factor analysis models with ordinal variables. The performance of PL is studied in terms of bias and mean squared error (MSE) and compared with that of the conventional estimation methods via a simulation study and through some real data examples. It is found that the PL estimates and standard errors have very small bias and MSE both decreasing with the sample size, and that the method is competitive to the conventional ones. The results of the first two papers lead to the next one where PL estimation is adjusted to the unrestricted Thurstonian ranking model. As before, the performance of the proposed approach is studied through a simulation study with respect to relative bias and relative MSE and in comparison with the conventional estimation methods. The conclusions are similar to those of the second paper. The last paper extends the PL estimation to the whole structural equation modeling framework where data may include both ordinal and continuous variables as well as covariates. The approach is demonstrated through an example run in R software. The code used has been incorporated in the R package lavaan (version 0.5-11)