Njål Foldnes

The flipped classroom and cooperative learning: Evidence from a randomised experiment:

This article describes a study which compares the effectiveness of the flipped classroom relative to the traditional lecture-based classroom. We investigated two implementations of the flipped classroom. The first implementation did not actively encourage cooperative learning, with students progressing through the course at their own pace. With this implementation, student examination scores did not differ between the lecture classes and the flipped classroom. The second implementation was organised with cooperative learning activities. In a randomised control-group pretest-posttest experiment, student scores on a post-test and on the final examination were significantly higher for the flipped classroom group than for the control group receiving traditional lectures. This demonstrates that the classroom flip, if properly implemented with cooperative learning, can lead to increased academic performance.

A note on hop-constrained walk polytopes

A hop-constrained walk is a walk with at most H arcs. The cases H=<3 have been addressed previously. Here, we consider the case H=4. We present an extended formulation for 4-walks and use the projection theorem of Balas and Pulleyblank to derive a complete linear description of the 4-walk polytope.

How general is the Vale-Maurelli simulation approach?

The Vale–Maurelli (VM) approach to generating non-normal multivariate data involves the use of Fleishman polynomials applied to an underlying Gaussian random vector. This method has been extensively used in Monte Carlo studies during the last three decades to investigate the finite-sample performance of estimators under non-Gaussian conditions. The validity of conclusions drawn from these studies clearly depends on the range of distributions obtainable with the VM method. We deduce the distribution and the copula for a vector generated by a generalized VM transformation, and show that it is fundamentally linked to the underlying Gaussian distribution and copula. In the process we derive the distribution of the Fleishman polynomial in full generality. While data generated with the VM approach appears to be highly non-normal, its truly multivariate properties are close to the Gaussian case. A Monte Carlo study illustrates that generating data with a different copula than that implied by the VM approach severely weakens the performance of normal-theory based ML estimates.

LP based heuristics for the multiple knapsack problem with assignment restrictions

Starting with a problem in wireless telecommunication, we are led to study the multiple knapsack problem with assignment restrictions. This problem is NP-hard. We consider special cases and their computational complexity. We present both randomized and deterministic LP based algorithms, and show both theoretically and computationally their usefulness for large-scale problems.

A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix.

ABSTRACT We present and investigate a simple way to generate nonnormal data using linear combinations of independent generator (IG) variables. The simulated data have prespecified univariate skewness and kurtosis and a given covariance matrix. In contrast to the widely used Vale-Maurelli (VM) transform, the obtained data are shown to have a non-Gaussian copula. We analytically obtain asymptotic robustness conditions for the IG distribution. We show empirically that popular test statistics in covariance analysis tend to reject true models more often under the IG transform than under the VM transform. This implies that overly optimistic evaluations of estimators and fit statistics in covariance structure analysis may be tempered by including the IG transform for nonnormal data generation. We provide an implementation of the IG transform in the R environment.

Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections

This simulation study investigates the performance of three test statistics, T1, T2, and T3, used to evaluate structural equation model fit under non normal data conditions. T1 is the well-known mean-adjusted statistic of Satorra and Bentler. T2 is the mean-and-variance adjusted statistic of Sattertwaithe type where the degrees of freedom is manipulated. T3 is a recently proposed version of T2 that does not manipulate degrees of freedom. Discrepancies between these statistics and their nominal chi-square distribution in terms of errors of Type I and Type II are investigated. All statistics are shown to be sensitive to increasing kurtosis in the data, with Type I error rates often far off the nominal level. Under excess kurtosis true models are generally over-rejected by T1 and under-rejected by T2 and T3, which have similar performance in all conditions. Under misspecification there is a loss of power with increasing kurtosis, especially for T2 and T3. The coefficient of variation of the nonzero eigenvalues of a certain matrix is shown to be a reliable indicator for the adequacy of these statistics.

The choice of product indicators in latent variable interaction models: post hoc analyses.

The unconstrained product indicator (PI) approach is a simple and popular approach for modeling nonlinear effects among latent variables. This approach leaves the practitioner to choose the PIs to be included in the model, introducing arbitrariness into the modeling. In contrast to previous Monte Carlo studies, we evaluated the PI approach by 3 post hoc analyses applied to a real-world case adopted from a research effort in social psychology. The measurement design applied 3 and 4 indicators for the 2 latent 1st-order variables, leaving the researcher with a choice among more than 4,000 possible PI configurations. Sixty so-called matched-pair configurations that have been recommended in previous literature are of special interest. In the 1st post hoc analysis we estimated the interaction effect for all PI configurations, keeping the real-world sample fixed. The estimated interaction effect was substantially affected by the choice of PIs, also across matched-pair configurations. Subsequently, a post hoc Monte Carlo study was conducted, with varying sample sizes and data distributions. Convergence, bias, Type I error and power of the interaction test were investigated for each matched-pair configuration and the all-pairs configuration. Variation in estimates across matched-pair configurations for a typical sample was substantial. The choice of specific configuration significantly affected convergence and the interaction tests outcome. The all-pairs configuration performed overall better than the matched-pair configurations. A further advantage of the all-pairs over the matched-pairs approach is its unambiguity. The final study evaluates the all-pairs configuration for small sample sizes and compares it to the non-PI approach of latent moderated structural equations.

The effect of kurtosis on the power of two test statistics in covariance structure analysis.

We study the effect of excess kurtosis on the non-centrality parameters of the rescaled and the residual-based test statistics for covariance structure models. The analysis is based on population matrices and parameters, which eliminates the sampling variability inherent in simulation studies. We show that the non-centrality parameters, and consequently the asymptotic power, decrease as kurtosis in the data increases. Examples are provided to compare this decrease for the two test statistics, and to illustrate how substantial it is.

The Asymptotic Covariance Matrix and its Use in Simulation Studies

The asymptotic performance of structural equation modeling tests and standard errors are influenced by two factors: the model and the asymptotic covariance matrix Γ of the sample covariances. Although most simulation studies clearly specify model conditions, specification of Γ is usually limited to values of univariate skewness and kurtosis. We illustrate that marginal skewness and kurtosis are not sufficient to adequately specify a nonnormal simulation condition by showing that asymptotic standard errors and test statistics vary substantially among distributions with skewness and kurtosis that are identical. We argue therefore that Γ should be reported when presenting the design of simulation studies. We show how Γ can be exactly calculated under the widely used Vale–Maurelli transform. We suggest plotting the elements of Γ and reporting the eigenvalues associated with the test statistic. R code is provided.

Covariance Model Simulation Using Regular Vines

We propose a new and flexible simulation method for non-normal data with user-specified marginal distributions, covariance matrix and certain bivariate dependencies. The VITA (VIne To Anything) method is based on regular vines and generalizes the NORTA (NORmal To Anything) method. Fundamental theoretical properties of the VITA method are deduced. Two illustrations demonstrate the flexibility and usefulness of VITA in the context of structural equation models. R code for the implementation is provided.