Parallel Time Series Analysis and Income Inequality: A New Approach to Comparative Case Studies

This case study deals with the role of time series analysis in sociology, and its relationship with the wider literature and methodology of comparative case study research. Time series analysis is now well-represented in top-ranked sociology journals, often in the form of ‘pooled time series’ research designs. These studies typically pool multiple countries together into a pooled time series cross-section panel, in order to provide a larger sample for more robust and comprehensive analysis. This approach is well suited to exploring trans-national phenomena, and for elaborating useful macro-level theories specific to social structures, national policies, and long-term historical processes. It is less suited however, to understanding how these global social processes work in different countries. As such, the complexities of individual countries - which often display very different or contradictory dynamics than those suggested in pooled studies – are subsumed. Meanwhile, a robust literature on comparative case-based methods exists in the social sciences, where researchers focus on differences between cases, and the complex ways in which they co-evolve or diverge over time. A good example of this is the inequality literature, where although panel studies suggest a general trend of rising inequality driven by the weakening power of labour, marketisation of welfare, and the rising power of capital, some countries have still managed to remain resilient. This case study takes a closer look at what can be learned by applying the insights of case-based comparative research to the method of time series analysis. Taking international income inequality as its point of departure, it argues that we have much to learn about the viability of different combinations of policy options by examining how they work in different countries over time. By taking representative cases from different welfare systems (liberal, social democratic, corporatist, or antipodean), we can better sharpen our theories of how policies can be more specifically engineered to offset rising inequality. This involves a fundamental realignment of the strategy of time series analysis, grounding it instead in a qualitative appreciation of the historical context of cases, as a basis for comparing effects between different countries.

Comparing meta-analysis and ecological-longitudinal analysis in time-series studies: a case study of the effects of air pollution on mortality in three Spanish cities

The objective of this paper is to introduce a diVerent approach, called the ecological-longitudinal, to carrying out pooled analysis in time series ecological studies. Because it gives a larger number of data points and, hence, increases the statistical power of the analysis, this approach, unlike conventional ones, allows the complementation of aspects such as accommodation of random effect models, of lags, of interaction between pollutants and between pollutants and meteorological variables, that are hardly implemented in conventional approaches. Design—The approach is illustrated by providing quantitative estimates of the short-termeVects of air pollution on mortality in three Spanish cities, Barcelona,Valencia and Vigo, for the period 1992–1994. Because the dependent variable was a count, a Poisson generalised linear model was first specified. Several modelling issues are worth mentioning. Firstly, because the relations between mortality and explanatory variables were nonlinear, cubic splines were used for covariate control, leading to a generalised additive model, GAM. Secondly, the effects of the predictors on the response were allowed to occur with some lag. Thirdly, the residual autocorrelation, because of imperfect control, was controlled for by means of an autoregressive Poisson GAM. Finally, the longitudinal design demanded the consideration of the existence of individual heterogeneity, requiring the consideration of mixed models. Main results—The estimates of the relative risks obtained from the individual analyses varied across cities, particularly those associated with sulphur dioxide. The highest relative risks corresponded to black smoke in Valencia. These estimates were higher than those obtained from the ecological-longitudinal analysis. Relative risks estimated from this latter analysis were practically identical across cities, 1.00638 (95% confidence intervals 1.0002, 1.0011) for a black smoke increase of 10 μg/m3 and 1.00415 (95% CI 1.0001, 1.0007) for a increase of 10 μg/m3 of sulphur dioxide. Because the statistical power is higher than in the individual analysis more interactions were statistically significant,especially those among air pollutants and meteorological variables. Conclusions—Air pollutant levels were related to mortality in the three cities of the study, Barcelona, Valencia and Vigo. These results were consistent with similar studies in other cities, with other multicentric studies and coherent with both, previous individual, for each city, and multicentric studies for all three cities

Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

Ozone and Mortality: A Meta-Analysis of Time-Series Studies and Comparison to a Multi-City Study (The National Morbidity, Mortality, and Air Pollution Study)

While many time-series studies of ozone and daily mortality identified positive associations,others yielded null or inconclusive results. We performed a meta-analysis of 144 effect estimates from 39 time-series studies, and estimated pooled effects by lags, age groups,cause-specific mortality, and concentration metrics. We compared results to estimates from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS), a time-series study of 95 large U.S. cities from 1987 to 2000. Both meta-analysis and NMMAPS results provided strong evidence of a short-term association between ozone and mortality, with larger effects for cardiovascular and respiratory mortality, the elderly, and current day ozone exposure as compared to other single day lags. In both analyses, results were not sensitive to adjustment for particulate matter and model specifications. In the meta-analysis we found that a 10 ppb increase in daily ozone is associated with a 0.83 (95% confidence interval: 0.53, 1.12%) increase in total mortality, whereas the corresponding NMMAPS estimate is 0.25%(0.12, 0.39%). Meta-analysis results were consistently larger than those from NMMAPS,indicating publication bias. Additional publication bias is evident regarding the choice of lags in time-series studies, and the larger heterogeneity in posterior city-specific estimates in the meta-analysis, as compared with NMAMPS.

Distribution of macrozooplankton at time series station MIGZOO-4

A large population of the colonial pelagic tunicate Pyrosoma atlanticum occurred in April 1991 in offshore waters of the Ligurian Sea (Northwestern Mediterranean). The high numbers of colonies caught allowed their vertical distribution and diel migration in the 0-965 m water column to be described as a function of their size. Daytime depths and amplitudes of the migration were correlated with colony size. The amplitude of the migration ranged from 90 m for 3-mm-length colonies to 760 m for 51-mm-length colonies, with a mean amplitude of 410 m for the whole population, all sizes pooled. The results of horizontal hauls at a given depth around sunrise and sunset showed a marked diurnal symmetry of the migratory cycle relative to noon, and that migration of the population was not cohesive. For example, the larger the colonies, the later after sunset they reached the upper layers during their upward migration.

Collection of data on particulate and dissolved soil nitrogen in the Jena Experiment (Main Experiment, time series since 2002)

This data set contains four time series of particulate and dissolved soil nitrogen measurements from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. 1. Total nitrogen from solid phase: Stratified soil sampling was performed every two years since before sowing in April 2002 and was repeated in April 2004, 2006 and 2008 to a depth of 30 cm segmented to a depth resolution of 5 cm giving six depth subsamples per core. In 2002 five samples per plot were taken and analyzed independently. Averaged values per depth layer are reported. In later years, three samples per plot were taken, pooled in the field, and measured as a combined sample. Sampling locations were less than 30 cm apart from sampling locations in other years. All soil samples were passed through a sieve with a mesh size of 2 mm in 2002. In later years samples were further sieved to 1 mm. No additional mineral particles were removed by this procedure. Total nitrogen concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany). 2. Total nitrogen from solid phase (high intensity sampling): In block 2 of the Jena Experiment, soil samples were taken to a depth of 1m (segmented to a depth resolution of 5 cm giving 20 depth subsamples per core) with three replicates per block ever 5 years starting before sowing in April 2002. Samples were processed as for the more frequent sampling but were always analyzed independently and never pooled. 3. Mineral nitrogen from KCl extractions: Five soil cores (diameter 0.01 m) were taken at a depth of 0 to 0.15 m (and between 2002 and 2004 also at a depth of 0.15 to 0.3 m) of the mineral soil from each of the experimental plots at various times over the years. In addition also plots of the management experiment, that altered mowing frequency and fertilized subplots (see further details below) were sampled in some later years. Samples of the soil cores per plot (subplots in case of the management experiment) were pooled during each sampling campaign. NO3-N and NH4-N concentrations were determined by extraction of soil samples with 1 M KCl solution and were measured in the soil extract with a Continuous Flow Analyzer (CFA, 2003-2005: Skalar, Breda, Netherlands; 2006-2007: AutoAnalyzer, Seal, Burgess Hill, United Kingdom). 4. Dissolved nitrogen in soil solution: Glass suction plates with a diameter of 12 cm, 1 cm thickness and a pore size of 1-1.6 µm (UMS GmbH, Munich, Germany) were installed in April 2002 in depths of 10, 20, 30 and 60 cm to collect soil solution. The sampling bottles were continuously evacuated to a negative pressure between 50 and 350 mbar, such that the suction pressure was about 50 mbar above the actual soil water tension. Thus, only the soil leachate was collected. Cumulative soil solution was sampled biweekly and analyzed for nitrate (NO3-), ammonium (NH4+) and total dissolved nitrogen concentrations with a continuous flow analyzer (CFA, Skalar, Breda, The Netherlands). Nitrate was analyzed photometrically after reduction to NO2- and reaction with sulfanilamide and naphthylethylenediamine-dihydrochloride to an azo-dye. Our NO3- concentrations contained an unknown contribution of NO2- that is expected to be small. Simultaneously to the NO3- analysis, NH4+ was determined photometrically as 5-aminosalicylate after a modified Berthelot reaction. The detection limits of NO3- and NH4+ were 0.02 and 0.03 mg N L-1, respectively. Total dissolved N in soil solution was analyzed by oxidation with K2S2O8 followed by reduction to NO2- as described above for NO3-. Dissolved organic N (DON) concentrations in soil solution were calculated as the difference between TDN and the sum of mineral N (NO3- + NH4+).

Collection of data on aboveground invertebrates in the Jena Experiment (time series since 2002)

This collection contains measurements of abundance and diversity of different groups of aboveground invertebrates sampled on the plots of the different sub-experiments at the field site of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. The following series of datasets are contained in this collection: 1. Measurements of ant abundance (number of individuals attracted to baits) and ant occurrence (binary data) in the Main Experiment in 2006 and 2013. Ants where sampled using two types of baited traps receiving ~10g of Tuna or ~10g of honey/Sucrose. After 30min the occurrence (presence = 1 / absence = 0) and abundance (number) of ants at the two types of baits was recorded and pooled per plot.

Time series analysis of a Web search engine transaction log

In this paper, we use time series analysis to evaluate predictive scenarios using search engine transactional logs. Our goal is to develop models for the analysis of searchers’ behaviors over time and investigate if time series analysis is a valid method for predicting relationships between searcher actions. Time series analysis is a method often used to understand the underlying characteristics of temporal data in order to make forecasts. In this study, we used a Web search engine transactional log and time series analysis to investigate users’ actions. We conducted our analysis in two phases. In the initial phase, we employed a basic analysis and found that 10% of searchers clicked on sponsored links. However, from 22:00 to 24:00, searchers almost exclusively clicked on the organic links, with almost no clicks on sponsored links. In the second and more extensive phase, we used a one-step prediction time series analysis method along with a transfer function method. The period rarely affects navigational and transactional queries, while rates for transactional queries vary during different periods. Our results show that the average length of a searcher session is approximately 2.9 interactions and that this average is consistent across time periods. Most importantly, our findings shows that searchers who submit the shortest queries (i.e., in number of terms) click on highest ranked results. We discuss implications, including predictive value, and future research.