Lecture
The essence of modeling consists in constructing models of the phenomena under study, which makes it possible to achieve a high degree of understanding of reality, and sometimes even to make precise quantitative predictions concerning the future development of the phenomena under study: that is, here the tasks of identifying connections between variables, of forecasting, and of control are solved.
The key notion is that of the model.
A model is a constructed object (physical or ideal) that reproduces certain properties of another object, which is the subject of study.
Modeling consists in constructing and further studying a model that replaces the direct study of the original object. The conclusions obtained in studying the model are transferred to the original object. A good model should be maximally simplified and should reflect the main properties of the original object.
The value of modeling lies in the fact that one can draw conclusions about phenomena that are difficult or impossible (dangerous) to study directly.
The process of creating a model consists of 3 stages: construction, fitting, and verification.
1. Construction – the description of the model using some language – natural or formal-logical. Models may be qualitative or quantitative. For constructing a model, the formulation of assumptions – that is, of decisions about the idealization of reality – is critically important.
2. At the fitting stage, various methods are used to determine the optimal values of the parameters, that is, the values that make it possible to bring the behavior of the model as close as possible to the behavior of the object being modeled.
3. Verification – the demonstration of the model's correspondence to the process under study, based on an evaluation of the model's ability to exhibit the predicted behavior under certain created conditions (we compare the behavior of the model and the object).
Quantitative evaluation of the degree of correspondence between the empirical and theoretical sets of data is carried out with the help of indices of fit. The choice of index depends on many conditions: the metric, the features of the distribution of the variables used. As a result of the check, a decision is made to accept or reject the model. The logic of testing models thus reveals an asymmetry of inference, like the testing of hypotheses in the experimental method.
Both modeling and the experimental method follow a hypothetico-deductive logic. Modeling is experimentation on models. In general form, a model represents a system of assertions about the connections between variables.
In contemporary psychology, sign modeling is used, which consists in constructing a formal model of psychical processes using symbolic systems. This is mathematical modeling. In the narrow sense, mathematical modeling is the description of the characteristics of objects in the form of equations:
1) dynamic modeling – describes the dynamics of complex systems with the help of the apparatus of differential equations;
2) Bayesian modeling – used for constructing quantitative models of cognitive processes, a constituent element of which is decision-making (the apparatus for testing hypotheses on the basis of Bayes' theorem).
Two variants of sign modeling significant for psychology:
1. computational modeling
The construction of a formal model of the phenomenon under study in the form of an executable computer program; this makes it possible to evaluate the behavior of complex models when obtaining such an evaluation by analytical means is difficult. For example, this is encountered in cognitive psychology.
2. statistical modeling
The construction of statistical models that give a compact description of a set of empirical data with insignificant loss of information. In general form, this is an equation describing the connections between one or several dependent variables and one or several independent variables. The ultimate goal is a quantitative description of the connections between psychological variables.
Variants:
- The linear regression model.
The researcher must specify the dependent variable (the criterion) and one or more independent variables (predictors). The model assumes that the value of the criterion represents a linear combination of the values of the predictors. By analyzing the parameters of this model, the researcher determines which predictors are important and which are not.
Example: a regression connecting success in passing an exam with a number of potential predictors (the number of hours of study, the student's appearance, their anxiety, and so on).
One needs to determine the values of the regression coefficients at the model-fitting stage; the method of least squares is used for fitting. At the verification stage: in the case of linear regression, the index of fit is the coefficient of multiple determination R^2; the value of this indicator is equal to the percentage of the variance of the criterion that can be explained by the combined influence of the predictors. High values of the coefficient indicate high model quality.
- The nonlinear regression model.
It allows for the presence of nonlinear connections between the criterion and the set of predictors.
- Multilevel (hierarchical) models
- Models with latent variables = unobservable factors that represent the variance common to several observed variables.
- Structural modeling. Here a combination of models with latent variables and regression models is used.
The problem of controlling the effect of data grouping. Hierarchical grouping. (pupil – class – school — district — city — region — country). Combination into nested groups such that at each level of nesting each unit belongs to only one group. The problem – a high degree of heterogeneity.
In analyzing the results of such studies, one should use hierarchical modeling.
Here the influence of the factors of each level is modeled by a separate equation, that is, the regression coefficients describing the effects of factors at a lower level themselves become the subject of modeling at a higher level. Advantages: the possibility of simultaneously estimating coefficients at different levels; taking into account differences in the precision of determining the effects of individual factors when estimating the effects of group factors => increased precision of the estimates of group and between-group interaction effects. High flexibility.
Difficulties of planning: one must determine the number of hierarchical levels that will be used in collecting and processing the data – usually there are 2 (the micro- and macro-levels); it is necessary to determine the number of factors included in the model at each level (it is better to take a few); heightened requirements at the stage of interpreting the results.
Comments