Estimates of heterogeneity (I2) can be biased in small meta-analyses

In meta-analysis, the fraction of variance that is due to heterogeneity is known as I2. We show that the usual estimator of I2 is biased. The bias is largest when a meta-analysis has few studies and little heterogeneity. For example, with 7 studies and the true value of I2 at 0, the average estimate of I2 is .124. Estimates of I2 should be interpreted cautiously when the meta-analysis is small and the null hypothesis of homogeneity (I2=0) has not been rejected. In small meta-analyses, confidence intervals may be preferable to point estimates for I2.Comment: 7 pages + 3 figure

Magnetospherically-trapped dust and a possible model for the unusual transits at WD 1145+017

The rapidly evolving dust and gas extinction observed towards WD 1145+017 has opened a real-time window onto the mechanisms for destruction-accretion of planetary bodies onto white dwarf stars, and has served to underline the importance of considering the dynamics of dust particles around such objects. Here it is argued that the interaction between (charged) dust grains and the stellar magnetic field is an important ingredient in understanding the physical distribution of infrared emitting particles in the vicinity of such white dwarfs. These ideas are used to suggest a possible model for WD 1145+017 in which the unusual transit shapes are caused by opaque clouds of dust trapped in the stellar magnetosphere. The model can account for the observed transit periodicities if the stellar rotation is near 4.5 h, as the clouds of trapped dust are then located near or within the co-rotation radius. The model requires the surface magnetic field to be at least around some tens of kG. In contrast to the eccentric orbits expected for large planetesimals undergoing tidal disintegration, the orbits of magnetospherically-trapped dust clouds are essentially circular, consistent with the observations.Comment: 5 pages, accepted to MNRAS Letter

New Confidence Intervals and Bias Comparisons Show that Maximum Likelihood Can Beat Multiple Imputation in Small Samples

When analyzing incomplete data, is it better to use multiple imputation (MI) or full information maximum likelihood (ML)? In large samples ML is clearly better, but in small samples ML's usefulness has been limited because ML commonly uses normal test statistics and confidence intervals that require large samples. We propose small-sample t-based ML confidence intervals that have good coverage and are shorter than t-based confidence intervals under MI. We also show that ML point estimates are less biased and more efficient than MI point estimates in small samples of bivariate normal data. With our new confidence intervals, ML should be preferred over MI, even in small samples, whenever both options are available.Comment: 5 table

Constraining the Surface Inhomogeneity and Settling Times of Metals on Accreting White Dwarfs

Due to the short settling times of metals in DA white dwarf atmospheres, any white dwarfs with photospheric metals must be actively accreting. It is therefore natural to expect that the metals may not be deposited uniformly on the surface of the star. We present calculations showing how the temperature variations associated with white dwarf pulsations lead to an observable diagnostic of the surface metal distribution, and we show what constraints current data sets are able to provide. We also investigate the effect that time-variable accretion has on the metal abundances of different species, and we show how this can lead to constraints on the gravitational settling times.Comment: 4 pages, 5 figures, accepted for publication in the Astrophysical Journal Letters, updated reference

Better estimates from binned income data: Interpolated CDFs and mean-matching

Researchers often estimate income statistics from summaries that report the number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+. Some analysts assign incomes to bin midpoints, but this treats income as discrete. Other analysts fit a continuous parametric distribution, but the distribution may not fit well. We fit nonparametric continuous distributions that reproduce the bin counts perfectly by interpolating the cumulative distribution function (CDF). We also show how both midpoints and interpolated CDFs can be constrained to reproduce the mean of income when it is known. We compare the methods' accuracy in estimating the Gini coefficients of all 3,221 US counties. Fitting parametric distributions is very slow. Fitting interpolated CDFs is much faster and slightly more accurate. Both interpolated CDFs and midpoints give dramatically better estimates if constrained to match a known mean. We have implemented interpolated CDFs in the binsmooth package for R. We have implemented the midpoint method in the rpme command for Stata. Both implementations can be constrained to match a known mean.Comment: 20 pages (including Appendix), 3 tables, 2 figures (+2 in Appendix