# Research Interests

My research interest covers several substantive areas, including human cooperation and coordination, as well as quantitative procedures for longitudinal research. All of my research flows from a framework that emphasizes the use of multiple types of models to provide convergent evidence for hypotheses in psychology and the social sciences. I begin below with an explanation of that framework, then move on to discussion of my substantive interests including examples of past and current research in each area.

## Convergent Models of Psychological Hypotheses

Why do we do science? Scientists and other researchers usually want to develop *models* of the way things work to understand the world and make predictions about what will happen in the future (or how to avoid things from happening). Models are simplifications of the world used for these purposes -- but as simplifications, they usually leave important things out, approximate uncertainties, and favor ease of understanding and use over exact recreations of reality. But we need these simplifications to operate -- Lewis Carroll satirized the idea of the perfect model through the idea of a map that was the same size as the area it represented; it could never be used because it blocked out the sunlight (and was probably a real problem to carry in the glove box, or whatever was the pre-automotive equivalent). We need to *reduce* problems to be able to *understand* them. A simpler way to say all of this is to quote Dr. Paul Smaldino and say "Models are stupid, and we need more of them."

If models are necessary simplifications of reality, then how do we use them to gain real understanding of the world? I argue, along with Dr. Smaldino, Dr. Jeff Schank, and Dr. William Wimsatt, among others, that it is by creating *multiple kinds* of models and using those models across *multiple experiments* that we can begin to understand processes. I use this philosophical framework to guide my research into substantive areas. Thus, this section of this page should be seen as background for understanding the approach I take to the more substantive research questions I discuss in the other three sections of this page.

There are four kinds of models that are in common use in the social sciences: conceptual models, physical models, mathematical models, and computational models.

**Conceptual models** are typically the first kind of model that a scientist will create. This is the basic statement or idea that drives further research; it is the one that you might tell someone outside your field if they ask you what your research is about (though it may require some translation and simplification). An example of a conceptual model is "* individuals in societies that organize into larger groups are likely to share less than those in societies with smaller groups*;" I will carry this example through the descriptions of all of the different kinds of models. Some of the benefits of conceptual models are that they are easy to communicate to a diverse audience, they are flexible, and they are inexpensive (often free!). However, they generally suffer from an important disadvantage: since they are usually informal, they can be vague, difficult to falsify, and subject to a wide range of unstated assumptions. Nonetheless, they are arguably the most important models since they are where most theory begins.

**Physical models** are the kinds of things that many people think of when they think of science. These are the real-world experiments, field studies, surveys, and other types of research that are performed with actual physical phenomena, people, and/or animals to generate, test, and validate our other kinds of models. An example of a physical model would be * a lab experiment testing how much people share when they are in different sized groups*. Another physical model would be a study correlating charitable donations with average community size across different US states. Some of the benefits of physical models are that experiments can provide strong evidence for cause and effect and that real-world models can involve the actual system of interest, which can be more convincing that mathematical abstractions or computer simulations. Physical models have their own disadvantages, though: they can be extremely expensive, they are often time-consuming, some kinds of research cannot be practically performed (for example, evolutionary theories require too much time for direct observation), and some research cannot be ethically performed (such as random-assignment experiments on drug abuse). An often-overlooked weakness of many physical models are hidden assumptions, such as the long tradition of using WEIRD research subjects and attempting to generalize the results to all humans or attempting to apply distant animal models like mice to humans (see the illuminating Twitter account @justsaysinmice). Even given these obstacles, though, physical models are important for testing the real-world truth and predictive power of our hypotheses.

**Mathematical models** are the point at which our models become *formal*, which is to say that entities and their relationships are methodically defined. In the case of a mathematical model, this takes the form of a mathematical formula or formulas (the word "formal" and "formula" are etymologically related). An very simple example of a mathematical model would be * s = a + bg*, where

*s*is the amount of sharing in a given society,

*a*is the average across different societies,

*g*is the size of groups in the given society, and

*b*is the magnitude of the effect of group size on sharing. Mathematical models can be explanatory, like this example, or data analytic. Explanatory models are a mathematical statement of the way we think the world works, and can be used to generate or simulate the data we expect to see in the real-world system. Data analytic models, also known as statistical models, are a way of analyzing data collected from a physical model to estimate unknown parameters in the model (like

*a*and

*b*in the example) or to test how well our mathematical model fits with real-world observations. One of the things that makes mathematical models so useful is that we can often turn an explanatory model directly (or almost directly) into a data-analytic model. Jack McArdle and others have argued that psychological researchers should avoid choosing a data-analytic model that is convenient or easy; instead, the most useful such models are derived from a mathematical model of how we think a process actually works. This is a perfect example of how different kinds of models can provide convergent evidence for a hypothesis. The previous example model, as simple as it is, can be converted to a data-analytic model very simply by added a term

*e*that represents the "noise" (also known as "unexplained variance") in the real-world data above and beyond the predictions of the explanatory model:

*. Even with these strengths, of course, mathematical models do have some disadvantages. Keeping the math simple enough to be solvable and understandable often leads to extreme simplifications of the real-world processes (our example models are excellent demonstrations of oversimplification). Turning a conceptual model into a mathematical model is often quite challenging, as is interpreting the meaning of a mathematical model (Richard McElreath has suggested that these might actually be the hardest parts of using these models). And, of course, these models also come with a large set of assumptions, such as the assumption common to the most-frequently used data-analytic models that the data come from a normal distribution. Still, given their formalism, explanatory power, and usefulness, science as we know it would not even be possible without mathematical models.*

**s = a + bg + e****Computational models** are simulations that explicitly describe rules of behavior and interactions. While these simulations are often run on computers, this is not a requirement ("computational" refers to the process, not the medium) -- one of the first such models in social science was realized on graph paper using coins to represent individuals. These include *agent-based models* (ABMs), which are powerful tools used to simulate individual behavior and interactions within groups. An example would be a simulation in which the simulated individuals can share reproductive resources with each other and evolve sharing and non-sharing behaviors with the ability to vary the group size. One of the most important advantages of computational models are that they explicitly model hypothesized mechanisms instead of only the mathematical implications of mechanisms, since mathematical patterns can theoretically result from multiple different mechanisms. Another strength is that assumptions are generally much more explicit in computational models than in other models; the processes are formally and thoroughly described in the rules that the simulation uses (whether a computer program or a list of actions to be taken by the simulator). Unknown quantities must explicitly be modeled (often by randomly generated distributions). Further, all information generated by the model is observable without unknown sources of error (which also implies that we can model the observational process itself to explore what biases and patterns are produced in real-world research with imperfect observation). Like all models, of course, computational models have their limitations. By themselves, simulations cannot be relied on to provide evidence that a mechanism *in silica* is the mechanism operating in the real world; we can provide arbitrary rules that produce behavior that is like that observed in the real world, but generated in a completely different way. Further, though these models are much more explicit in their assumptions, it is still possible that some hidden assumptions are present, particularly in the realm of omitted mechanisms. Despite these weaknesses, computational models provide some of the strongest evidence for why things work the way they do in terms of mechanisms and decision-making, especially when combined with physical models that allow us to alleviate the weaknesses of computational models.

It should be clear that the thread running through all of the model types is that they all have strengths and weaknesses. However, each type's weakness is complimented by a strength or potential test of one or more of the other models. Each type of model can generate new variations of the other types. More importantly, each type can be used to test the evidence from the others -- even a conceptual model can provide support or skepticism for another type of model in the form of asking, "Is this reasonable? Does this violate any principle that has wide support?" My central philosophy, then, is that we can do the best social science by developing convergent evidence across a mix of all of the types of model.

## Coordination

When individuals form collective patterns in space, we say they are coordinating. This idea of multiple individuals interacting in some way is, of course, also extended to domains that are not spatial; for example, we also say that people in different locations who are organizing a company's initial public offering are "coordinating." Coordination may be intentional, as in the latter case, or it may emerge without intentionality, as when grocery shoppers use their knowledge of crowding patterns at the store combined with the needs of their own schedule and kitchen to produce the highly predictable patterns of crowding at a given supermarket. (If you doubt the patterns are predictable, ask your personal supermarket's manager how she figures out how many employees should be scheduled for given times on given days.) How people make decisions about coordinating behavior is a question for the psychology of decision making, and one of the focuses of my research. In the past, I have explored how optimal-foraging theory leads to decisions to move between resources. I am currently researching how nearly-omniscient information (such as is available via cell phones) affects the choice and timing of using resources.

### Past Research in Coordination

Miller, M. L., Ringelman, K. M., Eadie, J. M., and Schank, J. C. (2017). Time to fly: A comparison of marginal value theorem approximations in an agent-based model of foraging waterfowl. Ecological Modelling, 351, 77-86.

### Current Research in Coordination

The Davis Beer Shoppe Problem: an exploration of how the classic El Farol Bar Problem plays out with pervasive information via agent-based modeling. How does the behavior of the consumer change? How does the pattern of resource use change?

## Cooperation

Cooperation and its maintenance was considered a conundrum in the evolution of behavior for many years. Fortunately, our understanding of evolutionary and social processes has advanced considerably in recent decades. Starting with Haldane and popularized by William Hamilton, kin selection and population viscosity were recognized as mechanisms by which cooperation could emerge; this was set on a firm mathematical basis that could be generalized to similar contexts by George Price. Further work has shown that punishment and other forms of coercion, covert signaling, and cultural norms and evolution can support cooperative behaviors. An excellent synthesis of many of these forces as they operate on human beings is given in A Cooperative Species by Bowles & Gintis. But cooperative behavior can be seen in organisms much less advanced than humans, and in humans seems to be robust beyond many of these predictions. Dr. Jeff Schank, Dr. Paul Smaldino, and I have begun to show that cooperation can emerge under a wide range of conditions as a simple mathematical property resulting from the constraints of multicellular life. Our prior research has shown that the reduction of resource variance in cooperative groups with minimal viscosity results in the evolution of cooperation. Our current research will show that cooperation is a simple matter of reducing inefficiency in the conversion of resources to offspring.

### Past Research in Cooperation

Schank, J. C., Smaldino, P. E., & Miller, M. L. (2015). Evolution of fairness in the dictator game by multilevel selection. Journal of Theoretical Biology, 382, 64-73.

### Current Research in Cooperation

Is Cooperation Just Efficiency? An early draft report of this research appears as the preprint "The evolution of fair offers with low rejection thresholds in the ultimatum game."

## Longitudinal Methods

To truly understand causal relationships in the social sciences, longitudinal methods are required. These methods are also vital in understanding developmental processes. While my training encompasses both static and dynamic methods with both discrete and continuous treatments of time, my methodological research thus far has been focused on longitudinal curve models in the structural equation modeling framework. These mathematical models provide an easy-to-interpret treatment of change over discrete time intervals. Given the discrete treatment of time, however, the common practice of allowing slight irregularities in the timing of data collection both between and within individuals is of concern. My past research looked at the general question of whether such irregularities are detectable via fit indices and how the irregularities affect identification of the true time course and model parameters. My current research examines effects on statistical efficiency and latent-basis estimation.

### Past Research in Longitudinal Methods

Miller, M. L., and Ferrer, E. (2017). The effect of sampling-time variation on latent growth curve models. Structural Equation Modeling: A Multidisciplinary Journal, 24, 831-854.

### Current Research in Longitudinal Methods

"Sampling-time variation, efficiency, and latent basis bias in latent curve models" - reporting of results in progress