Theory Construction Methodology: A Practical Framework for Building Theories in Psychology

This article aims to improve theory formation in psychology by developing a practical methodology for constructing explanatory theories: theory construction methodology (TCM). TCM is a sequence of five steps. First, the theorist identifies a domain of empirical phenomena that becomes the target of explanation. Second, the theorist constructs a prototheory, a set of theoretical principles that putatively explain these phenomena. Third, the prototheory is used to construct a formal model, a set of model equations that encode explanatory principles. Fourth, the theorist investigates the explanatory adequacy of the model by formalizing its empirical phenomena and assessing whether it indeed reproduces these phenomena. Fifth, the theorist studies the overall adequacy of the theory by evaluating whether the identified phenomena are indeed reproduced faithfully and whether the explanatory principles are sufficiently parsimonious and substantively plausible. We explain TCM with an example taken from research on intelligence (the mutualism model of intelligence), in which key elements of the method have been successfully implemented. We discuss the place of TCM in the larger scheme of scientific research and propose an outline for a university curriculum that can systematically educate psychologists in the process of theory formation.

Survival analysis of an impulsive stochastic facultative mutualism system with saturation effect

A system of impulsive stochastic differential equations is proposed as a two-species facultative mutualism model subject to impulsive and two coupling noise source perturbations, in which the saturation effect is taken into account. A set of sufficient criteria for extinction (exponential extinction and extinction) and permanence (permanence in time average and stochastic permanence) of the system are established. Extensive simulation figures are demonstrated to support the theoretical findings. Meanwhile, we look at the effects of coupling white noises, impulses, intrinsic growth rates, intra-specific competition rates and inter-specific mutualism rates on the survival of populations.

Analysis of a mutualism model with time-related coefficients in a stochastic environment

In this paper, a mutualism model with stochastic perturbations is considered and some of its coefficients are related to time. Under some assumptions, we make efforts to prove the existence and uniqueness of a positive solution, and the asymptotic behavior to the problem is discussed. Furthermore, we also prove the properties of stochastic boundedness, uniform continuity and stochastic permanence of this system. At last, some numerical simulations are introduced to illustrate our main results.

Permanence and extinction of stochastic regime-switching mutualism model

This paper is concerned with the permanence and extinction of a stochastic regime-switching mutualism model. We aim to find the difference between the stochastic mutualism model with regime-switching and without regime-switching. By studying ergodicity of regime-switching diffusion processes, we establish the sufficient conditions to estimate the permanence and extinction of a species in a random switching environment. Moreover, compared with the system without switching, the advantages of the stochastic regime-switching mutualism model are given.