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The authors go on to indicate that most studies of the relationship between perceived neighborhood safety and obesity have been limited primarily because they have been cross-sectional, though this is their design as well. The authors essentially assert that the two-stage least squares methodology enables them to sufficiently overcome biases of reverse causality and unmeasured confounders. As Freedman2 pointed out, two-stage least squares models are 20th-century versions of philosophers' stones in the futile though continual search for statistical models that, in the absence of proper study design features, will speak definitively to very complex causal questions in the social sciences.

Freedman was the author or co-author of 200 articles, 20 technical reports and six books, including a highly innovative and influential introductory statistics textbook, Statistics (2007), with Robert Pisani and Roger Purves, which has gone through four editions. The late Amos Tversky of Stanford University observed that "This is a great book. It is the best introduction to how to think about statistical issues...." It has a "wealth of real-world examples that illuminate principles and applications....a classic." Freedman's Statistical Models: Theory and Practice (2005) is an advanced text on statistical modeling that likewise achieves a remarkable integration between extensive examples and statistical theory.

Implementation science has progressed towards increased use of theoretical approaches to provide better understanding and explanation of how and why implementation succeeds or fails. The aim of this article is to propose a taxonomy that distinguishes between different categories of theories, models and frameworks in implementation science, to facilitate appropriate selection and application of relevant approaches in implementation research and practice and to foster cross-disciplinary dialogue among implementation researchers.

Theoretical approaches used in implementation science have three overarching aims: describing and/or guiding the process of translating research into practice (process models); understanding and/or explaining what influences implementation outcomes (determinant frameworks, classic theories, implementation theories); and evaluating implementation (evaluation frameworks).

However, the last decade of implementation science has seen wider recognition of the need to establish the theoretical bases of implementation and strategies to facilitate implementation. There is mounting interest in the use of theories, models and frameworks to gain insights into the mechanisms by which implementation is more likely to succeed. Implementation studies now apply theories borrowed from disciplines such as psychology, sociology and organizational theory as well as theories, models and frameworks that have emerged from within implementation science. There are now so many theoretical approaches that some researchers have complained about the difficulties of choosing the most appropriate [6-11].

It was possible to identify three overarching aims of the use of theories, models and frameworks in implementation science: (1) describing and/or guiding the process of translating research into practice, (2) understanding and/or explaining what influences implementation outcomes and (3) evaluating implementation. Theoretical approaches which aim at understanding and/or explaining influences on implementation outcomes (i.e. the second aim) can be further broken down into determinant frameworks, classic theories and implementation theories based on descriptions of their origins, how they were developed, what knowledge sources they drew on, stated aims and applications in implementation science. Thus, five categories of theoretical approaches used in implementation science can be delineated (Table 1; Figure 1):

Process models are used to describe and/or guide the process of translating research into practice. Models by Huberman [40], Landry et al. [41], the CIHR (Canadian Institutes of Health Research) Knowledge Model of Knowledge Translation [42], Davis et al. [43], Majdzadeh et al. [44] and the K2A (Knowledge-to-Action) Framework [15] outline phases or stages of the research-to-practice process, from discovery and production of research-based knowledge to implementation and use of research in various settings.

Early research-to-practice (or knowledge-to-action) models tended to depict rational, linear processes in which research was simply transferred from producers to users. However, subsequent models have highlighted the importance of facilitation to support the process and placed more emphasis on the contexts in which research is implemented and used. Thus, the attention has shifted from a focus on production, diffusion and dissemination of research to various implementation aspects [21].

The how-to-implement models typically emphasize the importance of careful, deliberate planning, especially in the early stages of implementation endeavours. In many ways, they present an ideal view of implementation practice as a process that proceeds step-wise, in an orderly, linear fashion. Still, authors behind most models emphasize that the actual process is not necessarily sequential. Many of the action models mentioned here have been subjected to testing or evaluation, and some have been widely applied in empirical research, underscoring their usefulness [9,55].

Implementation researchers are also wont to apply theories from other fields such as psychology, sociology and organizational theory. These theories have been referred to as classic (or classic change) theories to distinguish them from research-to-practice models [45]. They might be considered passive in relation to action models because they describe change mechanisms and explain how change occurs without ambitions to actually bring about change.

Another theory used in implementation science, the Normalization Process Theory [120], began life as a model, constructed on the basis of empirical studies of the implementation of new technologies [121]. The model was subsequently expanded upon and developed into a theory as change mechanisms and interrelations between various constructs were delineated [122]. The theory identifies four determinants of embedding (i.e. normalizing) complex interventions in practice (coherence or sense making, cognitive participation or engagement, collective action and reflexive monitoring) and the relationships between these determinants [123].

Although considerable growth of interest in SEM models was caused largely thanks to the works of Goldberger (1971, 1972) and to the publication titled Structural Equation Models in Social Sciences (Goldberger and Duncan 1973), which was the effect of an interdisciplinary conference organized in 1970 featuring economists, sociologists, psychologists, statisticians, and political scientists (from the Social Science Research Council) that was devoted to issues of structural equation models, in practice the true development of structural models results from the dynamic development of statistical software and synthetic combination of measurement models with structural models, which was expanded in the field of psychometrics and econometrics. Interestingly, although the methodological concepts related to SEM which appeared in the works of Jöreskog (1970, 1973), Keesling (1972) and Wiley (1973) were independently proposed (i.e., the studies were simultaneously conducted by the three researchers), in the literature mainly Jöreskog (1973) has been credited with the development of the first SEM model (including computer software (LISREL).

The transformations that SEM has experienced in recent years have caused further generalizations of this analytical strategy. Thanks to the works of Bartholomew (1987), Muthén (1994, 2001, 2002) and Skrondal and Rabe-Hesketh (2004), SEM has become a very general latent variable model which, together with the linear mixed model/hierarchical linear model, is the most widely recognized statistical solution in the social sciences (see the works of Muthén and Satorra 1995; MacCallum and Austin 2000; Stapleton 2006). Most of these contemporary advancements were made in the area of latent growth curve and latent class growth models for longitudinal data, the Bayesian method, multi-level SEM models, meta-SEM-analyses, multi-group SEM models, or algorithms adopted from artificial intelligence in order to discover the causal structure within the SEM framework. Below we will discuss some of these contemporary developments.

Bayesian analysis brought many benefits to SEM. One of them is the opportunity to learn from the data and to incorporate new knowledge into future investigations. Scholars need not necessarily rely on the notion of repeating an event (or experiment) infinitely as in the conventional (i.e., frequentist) framework; instead, they can combine prior knowledge with personal judgment in order to aid the estimation of parameters. The key difference between Bayesian statistics and conventional (e.g., ML estimator) statistics is the nature of the unknown parameters in the statistical model (Van de Schoot and Depaoli 2014). Also, the Bayesian method helped to improve the estimation of complex models, including those with random effect factor loadings, random slopes (when the observed variables are categorical), and three-level latent variable models that have categorical variables (Muthén 2010). On the other hand, Bayesian estimation which is based on Markov chain Monte Carlo algorithms has proved its usefulness in models with nonlinear latent variables (Arminger and Muthén 1998) or multi-level latent variable factor models (Goldstein and Browne 2002), and those which can be generated on the basis of a semiparametric estimator (Yang and Dunson 2010). Moreover, Bayesian estimation has helped to obtain impossible parameter estimates, thus aiding model identification (Kim et al. 2013), producing more accurate parameter estimates (Depaoli 2013) and aiding situations in which only small sample sizes are available (Zhang et al. 2007; Kaplan and Depaoli 2013). Also, with the Bayesian approach to SEM, researchers may favorably present their empirical research, e.g., in the confidence interval (CI) (Scheines et al. 1999). 2b1af7f3a8