Single Lag Research Articles

Regression analysis of longitudinal binary data with time-dependent environmental covariates: bias and efficiency

Generalized estimating equations (Liang and Zeger, 1986) is a widely used, moment-based procedure to estimate marginal regression parameters. However, a subtle and often overlooked point is that valid inference requires the mean for the response at time t to be expressed properly as a function of the complete past, present, and future values of any time-varying covariate. For example, with environmental exposures it may be necessary to express the response as a function of multiple lagged values of the covariate series. Despite the fact that multiple lagged covariates may be predictive of outcomes, researchers often focus interest on parameters in a 'cross-sectional' model, where the response is expressed as a function of a single lag in the covariate series. Cross-sectional models yield parameters with simple interpretations and avoid issues of collinearity associated with multiple lagged values of a covariate. Pepe and Anderson (1994), showed that parameter estimates for time-varying covariates may be biased unless the mean, given all past, present, and future covariate values, is equal to the cross-sectional mean or unless independence estimating equations are used. Although working independence avoids potential bias, many authors have shown that a poor choice for the response correlation model can lead to highly inefficient parameter estimates. The purpose of this paper is to study the bias-efficiency trade-off associated with working correlation choices for application with binary response data. We investigate data characteristics or design features (e.g. cluster size, overall response association, functional form of the response association, covariate distribution, and others) that influence the small and large sample characteristics of parameter estimates obtained from several different weighting schemes or equivalently 'working' covariance models. We find that the impact of covariance model choice depends highly on the specific structure of the data features, and that key aspects should be examined before choosing a weighting scheme.

Membrane Lateral Mobility Obstructed by Polymer-Tethered Lipids Studied at the Single Molecule Level

Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single molecule fluorescence microscopy. The obstacles are well-controlled concentrations of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer molecules is well described by a percolating system with different percolation thresholds for lipids and proteins. Data analysis using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calculations reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concentrations. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the analysis of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concentrations of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few molecules.

Blind adaptive channel shortening by single lag autocorrelation minimisation

A blind adaptive channel shortening algorithm based on minimising the sum of the squared autocorrelations (SAM) of the effective channel was recently proposed. We submit that essentially identical channel shortening can be achieved by minimising the square of only a single autocorrelation. Our proposed single lag autocorrelation minimisation (SLAM) algorithm has very low complexity. We also constrain the autocorrelation minimisation with a novel stopping criterion so that the shortening signal-to-noise ratio (SSNR) of the effective channel is not minimised by the autocorrelation minimisation. The simulations show that SLAM achieves higher bit rates than SAM.

Testing for the New Keynesian Phillips Curve. Additional international evidence

The “New Keynesian” Phillips Curve (NKPC) states that inflation has a purely forward-looking dynamics. In this paper, we test whether the inflation dynamics in European countries can be adequately described by this model. For this purpose, we estimate hybrid Phillips curves, which include both backward- and forward-looking components, for major European countries, the euro area, and the US. Using both GMM and ML estimation procedures, we examine the sensitivity of the estimates to the choice of output gap or real unit labor cost (ULC) as forcing variable and to the number of lags and leads in the inflation dynamics. Then, we provide several specification tests for the models estimated. Our findings can be summarized as follows. First, the forward-lookingness of the inflation dynamics is not altered by the choice of the forcing variable. In contrast, it is strongly affected by the lag and lead structure of inflation. Two specifications emerge: the real ULC specification with a single lag and lead and a large forward-looking component which is relevant in the US and the UK. The output gap specification with three lags and leads and a low degree of forward-lookingness provides a better fit for continental Europe.

Subtalar Joint Arthrodesis Using a Single Lag Screw

This study tested the hypotheses that fusing the subtalar joint with a single lag screw from the posteroinferior calcaneus to the anterior talar neck is an effective technique and that factors affecting the time to fusion can be identified. Between October, 1995, and July, 2002, the senior author (RAM) performed 101 isolated subtalar arthrodeses using a technique of single lag-screw fixation from posteroinferior to anterosuperior across the posterior facet of the subtalar joint combined with the application of an autograft taken from the floor of the sinus tarsi and anterior process. The average patient age was 52 (range 17 to 82) years. There were 52 women (53 arthrodeses) and 48 men (48 arthrodeses). Eight of 101 (8%) arthrodeses were revisions. The indications included posttraumatic arthritis (45), posterior tibial tendon dysfunction (18), failed prior ankle joint fusion (14), idiopathic disorders (12), hindfoot coalition (7), rheumatoid arthritis (3), and Charcot-Marie-Tooth disease (2). Fifteen of 101 patients (15%) smoked an average of 0.9 +/- 0.5 pack of cigarettes per day. Two of 101 joints did not fuse, resulting in an overall fusion rate of 98%. The average time to fusion was 12.3 +/- 3.4 weeks. The presence of a prior ankle fusion significantly prolonged the time to fusion of the subtalar joint (11.9 +/- 2.3 vs. 14.9 +/- 7.0, p = .003). Other factors, including smoking, revision surgery, patient age, and patient sex, did not affect time to fusion. The fixation screw was removed in 13 of 101 (13%) joints at an average of 8.8 +/- 0.5 months. Using a single 7.0-mm lag screw across the posterior facet of the subtalar joint results in fusion of the subtalar joint in 98% of patients. A prior ankle arthrodesis delays the time to fusion of the subtalar joint by 3 weeks. This is a simple and reliable technique for achieving fusion of the subtalar joint.

Superlinear population encoding of dynamic hand trajectory in primary motor cortex.

Neural activity in primary motor cortex (MI) is known to correlate with hand position and velocity. Previous descriptions of this tuning have (1) been linear in position or velocity, (2) depended only instantaneously on these signals, and/or (3) not incorporated the effects of interneuronal dependencies on firing rate. We show here that many MI cells encode a superlinear function of the full time-varying hand trajectory. Approximately 20% of MI cells carry information in the hand trajectory beyond just the position, velocity, and acceleration at a single time lag. Moreover, approximately one-third of MI cells encode the trajectory in a significantly superlinear manner; as one consequence, even small position changes can dramatically modulate the gain of the velocity tuning of MI cells, in agreement with recent psychophysical evidence. We introduce a compact nonlinear "preferred trajectory" model that predicts the complex structure of the spatiotemporal tuning functions described in previous work. Finally, observing the activity of neighboring cells in the MI network significantly increases the predictability of the firing rate of a single MI cell; however, we find interneuronal dependencies in MI to be much more locked to external kinematic parameters than those described recently in the hippocampus. Nevertheless, this neighbor activity is approximately as informative as the hand velocity, supporting the view that neural encoding in MI is best understood at a population level.

Intramedullary nails with two lag screws

Objective. To investigate the structural integrity of intramedullary nails with two lag screws, and to give guidance to orthopaedic surgeons in the choice of appropriate devices. Design. Alternative designs of the construct are considered, and the use of a slotted upper lag screw insertion hole is analysed. Background. Intramedullary fixation devices with a single lag screw have been known to fail at the lag screw insertion hole. Using two lag screws is considered. It has also been proposed to use a slot in the nail for the upper lag screw to prevent the upper lag screw from sticking. Methods. Bending and torsion load cases are analysed using finite element method. Consideration of both load conditions is essential. Results. The results present the overall stiffness of the assembly, the load sharing between lag screws, and the possibility for cut-out to occur. Conclusions. While the slot for the upper lag screw might be advantageous with regard to the stresses in the lag screws, it could be detrimental for cut-out occurring adjacent to the lag screws. Relevance Comparative analyses demonstrate that two lag screws may be advantageous in patients whose cancellous bone quality is good and who impose large loads on the lag screw/nail interface. However, the use of two screws might pre-dispose to failure by cut-out of the lag screws. The addition of a slotted hole for the upper lag screw appears to do nothing significant to reduce the risk of such a failure.

WIGGLE WORRY

Introduction The principle complexity in time series studies of dependence of mortality on air pollution arises from the need to disentangle the effect of air pollution from the usually larger variations of death counts over time due to other factors. Entering specific variables, such as temperature, humidity, and influenza reports alongside pollution in a Poisson regression of daily death count on air pollution helps, but leaves residual variation that can confound the pollution effect. To reduce this risk, investigators usually include in models terms for slow changes in mortality over time, using a variety of forms including moving averages, stratification, trigonometric functions of time, LOESS smooths, smoothing or natural cubic splines, or by case-crossover matching. For all of these, investigators must choose how wiggly to allow this nuisance term to be, for example choose degrees of freedom (df) in a smoothing spline. Insufficient wiggles (df) can leave residual confounding. Too many wiggles (df) can leave insufficient information from which to estimate the pollution effect coefficient, and exacerbate bias to the null caused by errors in mismeasuring or mismodelling air pollution. (A common form of mismodelling is when single pollution lag is used as proxy for a distributed lag effect.) Extent of wigglyness (df) has been decided by a priori judgement and a variety of data-based methods, including minimising AIC, absolute autocorrelation in residuals, or other test statistics for departure of residuals from white noise. Methods We have examined the properties of such methods by reference to simple principles and by simulation. Results General principles suggest that data-based methods can never determine whether a model (i.e. a specific wiggliness) is sufficient to control confounding bias, though impact of wiggliness on precision can be predicted given exposure series. Simulations confirm that in some realistic situations, application of any of the data-based criteria mentioned above can leave bias in pollution coefficients that is reduced if wiggliness of the time function is increased. Further, in the absence of mismeasurement/mismodelling of air pollution, using large numbers of df does not in general cause bias in the pollution coefficient, even if negative autocorrelation in residuals is induced. However, simulations also confirm negative consequences of increasing wiggles (df): (i) precision can be lost, though often not substantially, and (ii) bias due to mismeasuring or mismodelling pollution can be increased. Conclusions In the absence of mismeasurement/mismodelling of pollution, choice of smoothness in time functions comprises a simple trade-off between reduced vulnerability to confounding bias against reduced precision. In the presence of classical pollution measurement error or an imperfectly modelled pollution effect, however, adding more df to the time function also increases bias to the null of the pollution effect.

AVULSION FRACTURES FROM THE BASE OF THE PROXIMAL PHALANGES OF THE FINGERS

Thirty-three patients with avulsion fractures from the base of the proximal phalanges were treated during a 6-year period. All eight fractures treated conservatively failed to unite and subsequently required surgery. The remaining 25 patients were treated with primary internal fixation using a single lag screw through a palmar approach. Surgery gave excellent results in all cases and all patients achieved a full range of movement within 3 weeks.

Spectrum Widths from Echo Power Differences Reveal Meteorological Features

Abstract A new Doppler spectrum width estimator using the absolute power differences (APDs) at lag one is presented, and its performance is evaluated using simulated signals as well as those recorded from the National Severe Storms Laboratory's Research and Development WSR-88D. The APD estimate bias, its standard error of estimation, and the frequency of complex widths are compared with that obtained with other single lag estimators [e.g., the pulse-pair logarithm (PPL) estimator]. For narrow spectra and signal-to-noise ratios more than 15 dB, the APD estimator has lower bias, lower standard deviation, and a lesser number of complex width estimates than the PPL estimator. Spectrum width fields, observed when this estimate technique is applied to the logarithms of echo power from an X-band radar, reveal meteorologically significant features that are not often seen in weather radar displays in regions of relatively small spectrum widths.

Intramedullary femoral nails: one or two lag screws? A preliminary study

Failures of proximal femoral nails that treat unstable femoral fractures have been reported. In this communication, a finite element model to include a proximal femoral nail within a fractured femur was used to carry out preliminary investigations into configurations of single or double lag screws. The effects of the different types of fracture were investigated. The results show that in order to share the load evenly between two lag screws, a good configuration seems to be to have a slightly larger screw above the lower screw. This also ameliorates stresses in the nail at the lag screw insertion holes. However, using two screws in this way can lead to large stresses in the cancellous bone in the femoral head, and these stresses may be significant in the initiation of cut-out.

A Closed-Form GARCH Option Valuation Model

This paper develops a closed-form option valuation formula for a spot asset whose variance follows a GARCH(p,q) process that can be correlated with the returns of the spot asset. It provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables. The single lag version of this model contains Heston's (1993) stochastic volatility model as a continuous-time limit. Empirical analysis on S&P500 index options shows that the out-of-sample valuation errors from the single lag version of the GARCH model are substantially lower than the ad hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) that uses a separate implied volatility for each option to fit to the smirk/smile in implied volatilties. The GARCH model remains superior even though the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices while the ad hoc Black-Scholes model is updated every period. The improvement is largely due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility.

A Closed-Form GARCH Option Valuation Model

This paper develops a closed-form option valuation formula for a spot asset whose variance follows a GARCH(p, q) process that can be correlated with the returns of the spot asset. It provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables. The single lag version of this model contains Heston's (1993) stochastic volatility model as a continuous-time limit. Empirical analysis on S&P500 index options shows that the out-of-sample valuation errors from the single lag version of the GARCH model are substantially lower than the ad hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) that uses a separate implied volatility for each option to fit to the smirk/smile in implied volatilities. The GARCH model remains superior even though the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices while the ad hoc Black-Scholes model is updated every period. The improvement is largely due to the ability of the GARCH model to simultaneously capture the correlation of volatility, with spot returns and the path dependence in volatility. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Management of acute odontoid fractures with single-screw anterior fixation.

Accepted management strategies for odontoid fractures include external immobilization and surgical stabilization using anterior or posterior approaches. Displaced Type II fractures and rostral Type III fractures are at high risk for nonunion. Anterior fixation of odontoid fractures with a single cortical lag screw is a relatively new technique that combines rigid internal stabilization with preservation of intrinsic C1-C2 motion. We retrospectively reviewed our series of 26 consecutive patients who underwent odontoid screw fixation, to further define the safety and efficacy of the technique. During a 5-year period, 26 patients presented with acute traumatic Type II odontoid fractures. Ten patients were female and 16 were male, with a mean age of 35 years. All patients underwent anterior odontoid screw fixation by the senior surgeon (RWH), within a mean of 3 days after injury. All patients were postoperatively maintained in external orthoses, for a mean of 7.2 weeks, and were monitored with serial clinical and radiographic examinations. With a mean follow-up period of 30 months, radiographic fusion was documented for 25 of 26 patients (96%). No complications related to the surgical approach were identified, and all patients remained in neurologically stable condition. Two complications (8%) were related to the instrumentation; one patient required external immobilization because of suboptimal screw placement, and one patient required posterior atlantoaxial arthrodesis because of inadequate fracture reduction. Single-screw anterior odontoid fixation was associated with a relatively low complication rate and a high fusion rate in this study. We think that this should be the preferred treatment method for acute Type II odontoid fractures.

Short-term associations between outdoor air pollution and mortality in London 1992-4.

OBJECTIVES: A previous study of the short term effects of air pollution in London from April 1987 to March 1992 found associations between all cause mortality and black smoke and...

Multi-Lagged Specification of the Ohlson Model

This paper extends the study by Bar-Yosef, Callen, and Livnat (BCL) (1996), in which they test the single lagged formulation of the Ohlson (1995) linear valuation model by assuming that book values, earnings, and dividends are the underlying primitives in a multi-lagged Garman-Ohlson (1980) framework. Unlike BCL who focus solely on the information dynamic, this paper estimates both the information dynamic and the valuation equation. Also, since Akaike's (1969a, 1969b) final prediction error (FPE) and Akaike's (1973, 1974) information criterion (AIC) are known to overfit in small samples, the lag structure specification in this study is estimated by the AICe criterion suggested by Hurvich and Tsai (1989, 1991, 1994) rather than by the FPE criterion of BCL. Furthermore, to bias the case against a multi-lagged structure, the maximum lag structure is limited to three lags per variable rather than the five lags of BCL. Utilizing the result that the lag structure of the information dynamic determines the lag structure of the valuation equation, the internal consistency of the model is evaluated from the estimated lag structures. The median lag structure for the valuation equation implied by the lag structure of the estimated information dynamic is found to be somewhat inconsistent with the median lag structure estimated directly from the valuation equation. Further testing on a stationary subsample suggests that the inconsistency may be induced by nonstationarities. Overall, the results indicate strongly that the modeling of earnings and book values in a linear valuation framework necessarily requires a multi-lagged formulation rather than the single lag formulation common to the empirical accounting literature.

Air pollution, pollens, and daily admissions for asthma in London 1987–92

BACKGROUNDA study was undertaken to investigate the relationship between daily hospital admissions for asthma and air pollution in London in 1987–92 and the possible confounding and modifying effects of airborne...

Exact tests in single equation autoregressive distributed lag models

For hypotheses on the coefficient values of the lagged-dependent variables in the ARX class of dynamic regression models, test procedures are developed which yield exact inference for given (up to an unknown scale factor) distribution of the innovation errors. They include exact tests on the maximum lag length, for structural change and on the presence of (seasonal or multiple) unit roots, i.e. they cover situations where usually asymptotic and non-exact t, F, AOC, ADF or HEGY tests are employed. The various procedures are demonstrated and compared in illustrative empirical models and the approach is critically discussed.

Robust control in the gap: a state-space solution in the presence of a single input delay

A solution is provided to the problem of (sub)optimal robust design in the gap for a system with a single input lag. The problem is shown to reduce to two matrix algebraic Riccati equations that solve an allied linear-quadratic-Gaussian/H/sub 2/ problem and a parameterized differential matrix Riccati equation. The analysis intertwines finite-dimensional delay equations and distributed abstract evolution models. The parameterized family of suboptimal compensators is presented in terms of a neutral equation model.

Root-mean-square miss distance of proportional navigation missile against sinusoidal target

The performance of a proportional navigation homing missile against a target performing a sinusoidal weave maneuver is evaluated. The missile's effectiveness is measured in terms of the root-mean-square miss distance over a set of engagements in which the initial phase of the target weave is uniformly distributed. Closed form solutions for the root-mean-square miss are derived for the case where the missile guidance system is modeled by a first-order lag and the lateral acceleration is unlimited. The analysis is then extended to include the effects of acceleration saturation and higher order missile dynamics. Comparisons are made between a first-order and a fifth-order guidance system, and the root-mean-square miss is determined numerically as a function of the interceptor's effective navigation gain, time constant and acceleration limit, and the target's weave amplitude and frequency. UTURE homing interceptor missiles will face new and unique challenges as the sophistication of the threat spectrum in- creases. Engagements against air targets can occur at both very low and very high altitudes, with the threats accidentally or intentionally performing weaving or spiraling maneuvers during their midcourse and terminal phases.14 The lateral displacement, acceleration ca- pability, and weave frequency of the target maneuver can greatly enhance the threat's ability to survive a counterattack. To counter this, the defensive missile must have sufficient lateral acceleration, guidance system time constant, and terminal homing time to achieve a high probability of intercept. Whereas the per- formance of the interceptor will be influenced by many scenario- dependent factors,58 a major consideration will be the fundamental response of the proportional navigation (PN) guidance system to the postulated target weave motion.9'10 In the general case, the target dynamics may involve arbitrary periodic motion in three dimensions. A useful starting point for analysis, however, is the response of the PN homing system to a single plane sinusoidal maneuver of constant amplitude and fre- quency. The phase angle of target weave, which is associated with initial conditions at the start of the missile's terminal guidance, can be treated as a random variable, uniformly distributed between 0 and 2n over a set of engagements. The missile's dynamics are approxi- mated by a simple first-order transfer function, and unlimited lateral acceleration capability is assumed. The miss distance can then be parameterized in terms of the effective PN navigation gain N, the missile time constant T, and the amplitude AT and frequency co of the target weave. This paper focuses on root-mean-square (rms) miss distance as a recommended measure of effectiveness in analyzing missile perfor- mance against weaving targets. This measure allows uncertainties in target phase characteristics to be accounted for in the terminal per- formance results. The weaving target problem was first addressed by Chadwick, 9 who determined analytical expressions for the rms miss distance of the single lag PN missile for values of N =2 and 3. Zarchan 10 employed adjoint theory and transfer function tech- niques to determine formulas for the peak miss distance against a weaving target for values of N between 3 and 6. The present paper derives general closed-form expressions for the rms miss distance against a sinusoidal target. New results are obtained for arbitrary