An investigator who plans to conduct experiments with multiple independent variables must decide whether to use a complete or reduced factorial design. This article advocates a resource management perspective on making this decision, in which the investigator seeks a strategic balance between service to scientific objectives and economy. Considerations in making design decisions include whether research questions are framed as main effects or simple effects; whether and which effects are aliased (confounded) in a particular design; the number of experimental conditions that must be implemented in a particular design and the number of experimental subjects the design requires to maintain the desired level of statistical power; and the costs associated with implementing experimental conditions and obtaining experimental subjects. In this article four design options are compared: complete factorial, individual experiments, single factor, and fractional factorial designs. Complete and fractional factorial designs and single factor designs are generally more economical than conducting individual experiments on each factor. Although relatively unfamiliar to behavioral scientists, fractional factorial designs merit serious consideration because of their economy and versatility.Keywords experimental design; fractional factorial designs; factorial designs; reduced designs; resource management Suppose a scientist is interested in investigating the effects of k independent variables, where k > 1. For example, Bolger and Amarel (2007) investigated the hypothesis that the effect of peer social support on performance stress can be positive or negative, depending on whether the way the peer social support is given enhances or degrades self-efficacy. Their experiment could be characterized as involving four factors: support offered (yes or no), nature of support (visible or indirect), message from a confederate that recipient of support is unable to handle Correspondence may be sent to Linda M. Collins, The Methodology Center, Penn State, 204 E. Calder Way, Suite 400, State College, PA 16801; LMCollins@psu.edu. NIH Public Access Author ManuscriptPsychol Methods. Author manuscript; available in PMC 2010 September 1. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript the task alone (yes or no), and message that a confederate would be unable to handle the task (yes or no).One design possibility when k > 1 independent variables are to be examined is a factorial experiment. In factorial research designs, experimental conditions are formed by systematically varying the levels of two or more independent variables, or factors. For example, in the classic two × two factorial design there are two factors each with two levels. The two factors are crossed, that is, all combinations of levels of the two factors are formed, to create a design with four experimental conditions. More generally, factorial designs can include k ≥ 2 factors and can incorporate two or more levels per factor. With four two-level var...

Selecting the number of different classes which will be assumed to exist in the population is an important step in latent class analysis (LCA). The bootstrap likelihood ratio test (BLRT) provides a data-driven way to evaluate the relative adequacy of a (K −1)-class model compared to a K-class model. However, very little is known about how to predict the power or the required sample size for the BLRT in LCA. Based on extensive Monte Carlo simulations, we provide practical effect size measures and power curves which can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters. Estimated power curves and tables provide guidance for researchers wishing to size a study to have sufficient power to detect hypothesized underlying latent classes.

Abstract Information criteria (ICs) based on penalized likelihood, such as Akaike’s information criterion (AIC), the Bayesian information criterion (BIC) and sample-size-adjusted versions of them, are widely used for model selection in health and biological research. However, different criteria sometimes support different models, leading to discussions about which is the most trustworthy. Some researchers and fields of study habitually use one or the other, often without a clearly stated justification. They may not realize that the criteria may disagree. Others try to compare models using multiple criteria but encounter ambiguity when different criteria lead to substantively different answers, leading to questions about which criterion is best. In this paper we present an alternative perspective on these criteria that can help in interpreting their practical implications. Specifically, in some cases the comparison of two models using ICs can be viewed as equivalent to a likelihood ratio test, with the different criteria representing different alpha levels and BIC being a more conservative test than AIC. This perspective may lead to insights about how to interpret the ICs in more complex situations. For example, AIC or BIC could be preferable, depending on the relative importance one assigns to sensitivity versus specificity. Understanding the differences and similarities among the ICs can make it easier to compare their results and to use them to make informed decisions.

Latent class analysis • Likelihood ratio testing • Model selection Key Points:• Information criteria such as AIC and BIC are motivated by different theoretical frameworks.• However, when comparing pairs of nested models, they reduce algebraically to likelihood ratio tests with differing alpha levels.• This perspective makes it easier to understand their different emphases on sensitivity versus specificity, and why BIC but not AIC possesses model selection consistency.• This perspective is useful for comparisons, but it does not mean that the information criteria are only likelihood ratio tests. Information criteria can be used in ways these tests themselves are not as well suited for, such as for model averaging.

Background An understanding of the individual and combined effects of a set of intervention components is important for moving the science of preventive medicine interventions forward. This understanding can often be achieved in an efficient and economical way via a factorial experiment, in which two or more independent variables are manipulated. The factorial experiment is a complement to the randomized controlled trial (RCT); the two designs address different research questions. Purpose This article offers an introduction to factorial experiments aimed at investigators trained primarily in the RCT. Method The factorial experiment is compared and contrasted with other experimental designs used commonly in intervention science to highlight where each is most efficient and appropriate. Results Several points are made: factorial experiments make very efficient use of experimental subjects when the data are properly analyzed; a factorial experiment can have excellent statistical power even if it has relatively few subjects per experimental condition; and when conducting research to select components for inclusion in a multicomponent intervention, interactions should be studied rather than avoided. Conclusions Investigators in preventive medicine and related areas should begin considering factorial experiments alongside other approaches. Experimental designs should be chosen from a resource management perspective, which states that the best experimental design is the one that provides the greatest scientific benefit without exceeding available resources.