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Lecturer(s)
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Dostál Daniel, PhDr. Ph.D.
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Course content
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Models and the modeling of reality - the role of models in scientific inquiry, the function of models in quantitative disciplines, and the relationship between reality and its mathematical or statistical representation. Simple linear regression and its graphical representation - fundamental principles of simple regression, parameter estimation, visualization of regression lines, and interpretation of relationships between variables. Standardized regression coefficients - the purpose of standardization, comparing the influence of individual predictors, and interpreting results across different variable scales. Assessing model quality - measures of model fit (R2, adjusted R2, residual analysis). Multiple linear regression - extending the simple model to include multiple predictors and interpreting partial coefficients. Categorical variables in linear models - coding categorical predictors, group comparisons, dummy variables, and contrasts. Interactions of factors - the meaning and interpretation of interaction effects, graphical presentation of interactions, and their use in modeling more complex relationships. Exploring nonlinear relationships - polynomial and transformed models. Statistical significance testing - principles of hypothesis testing in linear models, pvalues, and confidence intervals. Assumptions of linear models - key assumptions (normality, homoscedasticity, linearity, independence), diagnostic tools and procedures for their verification, and the identification of outliers or influential observations. Prediction and interval estimation - using models to forecast new values, prediction and confidence intervals, and interpreting their width and meaning. Mixed-effects models - introduction to hierarchical and multilevel models, random intercepts and slopes, and their application in the context of repeated measures and clustered data.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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The course is designed to address two closely interconnected dimensions. The first focuses on developing a deeper understanding of the role of models in scientific inquiry - recognizing the necessity of constructing models as tools for describing complex phenomena of the real world, and understanding both the strengths and the inherent limitations of this approach. Particular emphasis is placed on quantitative and statistical models, which provide a means to formulate and test hypotheses grounded in empirical data. The second dimension is aimed at systematically introducing students to a specific class of statistical models: linear models. These represent not only a highly versatile analytical tool applied across a wide range of scientific disciplines, but also serve as an essential entry point for understanding and eventually employing other, more advanced classes of statistical models. The course also emphasizes the development of practical skills: students will gain experience working with widely used specialized software for statistical data analysis. This will enable them not only to apply theoretical knowledge in practice but also to acquire hands-on expertise directly transferable to their future professional or research activities.
Upon successful completion of the course, students will be able to: - Model a wide range of problems using statistical linear models, assess the appropriateness of their application in specific research or practical contexts, and critically evaluate the results obtained. - Independently analyze quantitative data using selected statistical software, including data preparation, the choice of appropriate analytical procedures, and the interpretation of outputs. - Perform statistical predictions of operationalized phenomena based on historical data, assess the degree of uncertainty associated with such predictions, and recognize the limitations of the resulting conclusions. - Reflect on the methodological aspects of working with linear models, understand their underlying assumptions, and appreciate the implications of any violations for the validity of the results.
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Prerequisites
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Participation in the course presupposes that students possess at least a basic familiarity with quantitative methods. In particular, they are expected to have a fundamental understanding of the role of descriptive statistics in summarizing data, as well as a general awareness of the principles of statistical hypothesis testing, including a basic grasp of the meaning and interpretation of pvalues. These competencies are not the primary focus of the course; rather, they provide an essential foundation on which the instruction builds, enabling students to more effectively engage with the advanced topics covered in the course.
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Assessment methods and criteria
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unspecified
The course is concluded with an examination. To be eligible for it, students are required to complete a series of independent assignments throughout the semester. These assignments involve constructing statistical models based on specified instructions and performing selected computations on assigned datasets. Over the course of the semester, students work with more than twelve datasets and solve over sixty individual analytical tasks. To ensure independent work, each student is automatically provided with individualized datasets that differ from those of other participants. The results of their analyses are submitted and communicated via an interactive web interface, which also provides immediate feedback on correctness.
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Recommended literature
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Dostál, D. Lineární statistické modely v psychologii. .
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