Binscatter Regressions

We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg}, which implements the binscatter methods developed in \citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}. The first command (\texttt{binsreg}) implements binscatter for the regression function and its derivatives, offering several point estimation, confidence intervals and confidence bands procedures, with particular focus on constructing binned scatter plots. The second command (\texttt{binsregtest}) implements hypothesis testing procedures for parametric specification and for nonparametric shape restrictions of the unknown regression function. Finally, the third command (\texttt{binsregselect}) implements data-driven number of bins selectors for binscatter implementation using either quantile-spaced or evenly-spaced binning/partitioning. All the commands allow for covariate adjustment, smoothness restrictions, weighting and clustering, among other features. A companion \texttt{R} package with the same capabilities is also available

On Binscatter

Binscatter is very popular in applied microeconomics. It provides a flexible, yet parsimonious way of visualizing and summarizing large data sets in regression settings, and it is often used for informal evaluation of substantive hypotheses such as linearity or monotonicity of the regression function. This paper presents a foundational, thorough analysis of binscatter: we give an array of theoretical and practical results that aid both in understanding current practices (i.e., their validity or lack thereof) and in offering theory-based guidance for future applications. Our main results include principled number of bins selection, confidence intervals and bands, hypothesis tests for parametric and shape restrictions of the regression function, and several other new methods, applicable to canonical binscatter as well as higher-order polynomial, covariate-adjusted and smoothness-restricted extensions thereof. In particular, we highlight important methodological problems related to covariate adjustment methods used in current practice. We also discuss extensions to clustered data. Our results are illustrated with simulated and real data throughout. Companion general-purpose software packages for \texttt{Stata} and \texttt{R} are provided. Finally, from a technical perspective, new theoretical results for partitioning-based series estimation are obtained that may be of independent interest

Dual-Frequency Observations of 140 Compact, Flat-Spectrum Active Galactic Nuclei for Scintillation-Induced Variability

The 4.9 GHz Micro-Arcsecond Scintillation-Induced Variability (MASIV) Survey detected a drop in Interstellar Scintillation (ISS) for sources at redshifts z > 2, indicating an apparent increase in angular diameter or a decrease in flux density of the most compact components of these sources, relative to their extended emission. This can result from intrinsic source size effects or scatter broadening in the Intergalactic Medium (IGM), in excess of the expected (1+z)^0.5 angular diameter scaling of brightness temperature limited sources due to cosmological expansion. We report here 4.9 GHz and 8.4 GHz observations and data analysis for a sample of 140 compact, flat-spectrum sources which may allow us to determine the origin of this angular diameter-redshift relation by exploiting their different wavelength dependences. In addition to using ISS as a cosmological probe, the observations provide additional insight into source morphologies and the characteristics of ISS. As in the MASIV Survey, the variability of the sources is found to be significantly correlated with line-of-sight H-alpha intensities, confirming its link with ISS. For 25 sources, time delays of about 0.15 to 3 days are observed between the scintillation patterns at both frequencies, interpreted as being caused by a shift in core positions when probed at different optical depths. Significant correlation is found between ISS amplitudes and source spectral index; in particular, a large drop in ISS amplitudes is observed at spectral indices of < -0.4 confirming that steep spectrum sources scintillate less. We detect a weakened redshift dependence of ISS at 8.4 GHz over that at 4.9 GHz, with the mean variance at 4-day timescales reduced by a factor of 1.8 in the z > 2 sources relative to the z < 2 sources, as opposed to the factor of 3 decrease observed at 4.9 GHz. This suggests scatter broadening in the IGM.Comment: 30 pages, 14 figures, accepted for publication in the Astronomical Journa

Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant

The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this paper this data is fit to models for the equation of state with w = -1, w = const, and w(z) = w_0+w_a(1-a). The last model is poorly constrained by the distance data, leading to unphysical solutions where the dark energy dominates at early times unless the large scale structure and acoustic scale constraints are modified to allow for early time dark energy effects. A flat LambdaCDM model is consistent with all the data.Comment: 19 pages Latex with 8 Postscript figure files. A new reference and constraint, w vs w' contour plots updated. Version accepted by the the Ap

B and I-band optical micro-variability observations of the BL Lac objects S5 2007+777 and 3C371

We have observed S5 2007+777 and 3C371 in the B and I bands for 13 and 8 nights, respectively, during various observing runs in 2001, 2002 and 2004. The observations resulted in almost evenly sampled light curves, 6-9 hours long. We do not detect any flares within the observed light curves, but we do observe small amplitude, significant variations, in both bands, on time scales of hours and days. The average variability amplitude on time scales of minutes/hours is 2.5% and 1-1.5% in the case of S5 2007+777 and 3C371, respectively. The average amplitudes increase to 5-12% and 4-6%, respectively, on time scales of days. We find that the B and I band variations are highly correlated, on both short and long time scales. During the 2004 observations, which resulted in the longest light curves, we observe two well defined flux-decay and rising trends in the light curves of both objects. When the flux decays, we observe significant delays, with the B band flux decaying faster than the flux in the I band. As a result, we also observe significant, flux related spectral variations as well. The flux-spectral relation is rather complicated, with loop-like structures forming during the flux evolution. The presence of spectral variations imply that the observed variability is not caused by geometric effects. On the other hand, our results are fully consistent with the hypothesis that the observed variations are caused by perturbations which affect different regions in the jet of the sources.Comment: Accepted for publication in Astronomy and Astrophysic

Variability of the soft X-ray excess in IRAS 13224-3809

We study the soft excess variability of the narrow line Seyfert 1 galaxy IRAS 13224-3809. We considered all five archival XMM-Newton observations, and we applied the 'flux-flux plot' (FFP) method. We found that the flux-flux plots were highly affected by the choice of the light curves' time bin size, most probably because of the fast and large amplitude variations, and the intrinsic non-linear flux--flux relations in this source. Therefore, we recommend that the smallest bin-size should be used in such cases. Hence, We constructed FFPs in 11 energy bands below 1.7 keV, and we considered the 1.7-3 keV band, as being representative of the primary emission. The FFPs are reasonably well fitted by a 'power-law plus a constant' model. We detected significant positive constants in three out of five observations. The best-fit slopes are flatter than unity at energies below $\sim 0.9$ keV, where the soft excess is strongest. This suggests the presence of intrinsic spectral variability. A power-law-like primary component, which is variable in flux and spectral slope (as $\Gamma\propto N_{\rm PL}^{0.1}$) and a soft-excess component, which varies with the primary continuum (as $F_{\rm excess}\propto F_{\rm primary}^{0.46}$), can broadly explain the FFPs. In fact, this can create positive `constants', even when a stable spectral component does not exist. Nevertheless, the possibility of a stable, soft--band constant component cannot be ruled out, but its contribution to the observed 0.2-1 keV band flux should be less than $\sim 15$ %. The model constants in the FFPs were consistent with zero in one observation, and negative at energies below 1 keV in another. It is hard to explain these results in the context of any spectral variability scenario, but they may signify the presence of a variable, warm absorber in the source.Comment: Accepted for publication in A&A, 10 pages, 7 figure

Velocity dispersion in N-body simulations of CDM models

This work reports on a study of the spatially coarse-grained velocity dispersion in cosmological N-body simulations (OCDM and Lambda-CDM models) as a function of time (redshifts z=0-4) and of the coarsening length (0.6-20 Mpc/h). The main result is the discovery of a polytropic relationship I_1 ~ rho^{2-eta} between the velocity-dispersion kinetic energy density of the coarsening cells, I_1, and their mass density, rho. The exponent eta, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction eta_virial=0. This relationship supports the ``polytropic assumption'' which has been employed in theoretical models for the growth of cosmological structure by gravitational instability.Comment: Minor, unimportant changes. Matches published versio