Advanced Quantitative Methods, Trinity Term 2023

3rd May 2023 09:00 - 12:00 26th May 2023

Courses are now fully booked. If you would still like to register, we can place you on the waiting-list for each respective course.

In Trinity Term 2023 we will offer four in-person advanced quantitative methods courses at the Department of Education, University of Oxford. The first two course (multilevel and structural equation modelling) are open for all interested Department of Education students and members of staff. The later two courses (psychometrics and assessment analysis, and advanced modelling in R) have a limited number of places available for Masters and Doctoral students.

The courses require a basic understanding of multiple regression modelling or other multivariate techniques. We will use a variety of software, including R-studio, various R-modules, and Mplus (mostly the free demo-version) during the courses.

Students and staff are welcome to sign up using the following link oxfordeducation.eu.qualtrics.com/jfe/form/SV_8faQDVnVPLeJSvk

Our program is:
Oxford TT Week 2 Multilevel modelling (Ariel Lindorff)
Oxford TT Week 3 Structural equation modelling (Lars Malmberg):
Oxford TT Week 4 Psychometrics and assessment analysis (Chris Wheadon)
Oxford TT Week 5 Advanced models in R (Lars Malmberg)

Oxford TT Week 2
Multilevel modelling (Ariel Lindorff): Open to all students (and staff) in the Department of Education (Wed 3 May 2023, 9:30-12:30). We will meet in Seminar Room D (with online access as an alternative to joining in person). This workshop will build on participants’ existing knowledge of regression models, introducing multilevel models for hierarchically nested data. We will be working in R, primarily relying on the lme4 package. We will cover fixed, random and contextual effects, and learn how to visualise findings.

Oxford TT Week 3
Structural equation modelling (Lars Malmberg): Open to all students (and staff) in the department. We will convene 9-12 in person in Seminar Room D (with online access). Pre-recorded materials and example datasets and models (in R and Mplus) will be made available in advance. See further details of each day below.

Tue 9 May, 9-12 Intro Structural Equation Models (SEM)
Wed 10 May, 9-12 Longitudinal SEM
Fri 20 May, 9-12 Multilevel and intraindividual SEM

Oxford TT Week 4
Psychometrics and assessment analysis (Chris Wheadon): Up to seven departmental Masters and Doctoral students can audit the course. Participants will be selected based on closeness between own research and the course contents. Three major frameworks will be discussed and compared – Classical Test Theory, Comparative Judgement and Item Response Theory. The difference between the Bradley-Terry-Luce model as well as the 1-, 2- and 3-parameter logistic (PL) models will be examined. For IRT, the 1-PL model widely known as the Rasch model will be the focus. Advantages and disadvantages of the frameworks and different models will be overviewed, and implications of model choice will be discussed. Teaching will be in seminar rooms K/L from 9.30 to 5 on Monday (15/5), Tuesday (16/5) and Thursday (18/5), and 9-30 to 12-30 on Wednesday (17/5) and Friday (19/5).

Oxford TT Week 5
Advanced models in R (Lars Malmberg 22-26/5/2023): Up to seven departmental Masters and Doctoral students can audit the lecture part of the course (each morning 22-26/5). Participants will be selected based on closeness between own research and the course contents (see further details of each day below).

Students and staff who wish to engage in self-learning can have access to Canvas in which both the Intro QM and Intermediate QM courses now have extensive R (and SPSS) lecture and application materials (videos). Students can get access to all LM’s and AL’s advanced course materials for self-learning too.

 

Week 3 of Trinity Term Structural Equation Models

Introduction to Structural Equation Modelling 

Tue 9/5, 9-12 in Sem Room D, possibility to join online

Pre-recorded videos and materials made available in advance of the session

The concept of a latent construct is central in the social sciences. A latent construct is a non-directly observed phenomenon (e.g., attitude, socioeconomic status) that we can model using manifest (observed) variables (e.g., survey and questionnaire responses, observation scores), by partitioning out residual (i.e., uniqueness, error variance). The structural equation model (SEM) is divided into two parts. In the measurement part of the model, we can inspect whether manifest variables measure the constructs they are intended to measure. This model is called confirmatory factor analysis (CFA) which allows the researcher to test whether an a priori model fits data, and whether this also holds across multiple groups. If measurement is satisfactory, the relationships between constructs can be estimated in the structural part of the SEM. Complex relationships between manifest variables and/or latent constructs can be tested in path-models not possible to specify in the multiple regression framework. During the course we will cover worked examples relevant for educational, psychological and social sciences.

Pre-requirements 

Participants need to understand the basics of multiple regression, or other relevant multivariate statistics.

Contents 

Video-clip 1 Basic concepts, models and measurement. From multiple regression to path-models using manifest variables.

Video-clip 2 Observed (manifest) variables and unobserved (latent) constructs. Specification of measurement models for testing quality of measurement, using continuous and dichotomous manifest variables. Goodness-of-fit indices.

Demonstration video-clips. Models in R-lavaan
Demonstration video-clips. Models in Mplus

Program 

09.00-09.30 Recap of basics of SEM  (questions can be posted in the Q&A document)

09.30-10.30 Measurement models and goodness of fit

10.30-10.45 Break

10.45-12.00 Structural models for answering substantive research questions

Software: We will mainly use the Mplus demo https://www.statmodel.com/demo.shtml) software. Parallel code is available in R (Lavaan) (http://lavaan.org). Materials are made available in advance of the session, and can also be used for self-study.

 

Structural Equation Modelling of longitudinal data  

Wed 10/5, 9-12 in Sem Room D, possibility to join online

Pre-recorded videos and materials made available in advance of the session

In this follow-up of the introduction to SEM course we focus on SEM for longitudinal data. Prospective longitudinal data is typically collected over longer periods of time e.g., terms or years. Using SEM we can model repeated latent constructs over time using autoregressive models, that is a construct at the concurrent time-point regressed on that construct at a previous time-point. We can also test whether the measurement is invariant (measured in the same way) across the time-points. When particular interest is in individual differences in change over time, we can model time explicitly in the latent growth curve model. The worked examples are based on educational longitudinal data, relevant for social sciences.

Pre-requirements:

Participants need to understand the basics of multiple regression, other relevant multivariate statistics, and have some exposure to either regression or SEM.

Contents 

Video-clip 1: Introduction to longitudinal (repeated measures modelling)

Video-clip 2: Auto-regressive modelling

Video-clip 3: Growth modelling

Wednesday 18 May 

09.00-09.30 Recap of longitudinal modelling  (questions can be posted in the Q&A document)

09:30-10:30 Autoregressive modelling, and testing of measurement invariance

10.30-10.45 Break

10.45-12:00 Growth models

Software: We will use R Lavaan and Mplus software (full version, input and output files are available). Materials are made available in advance of the session, and can also be used for self-study.

 

Structural Equation Modelling for multilevel and intraindividual data 

Fri 12/5, 9-12 in Sem Room D, possibility to join online

Pre-recorded videos and materials made available in advance of the session

Multilevel structural equation modelling (MSEM) combines the best of two worlds, the multilevel model (MLM) and SEM. The multilevel SEM (MSEM) allows us to test structural validity in two or more hierarchical levels, and specify level-specific associations between level-specific predictors and outcomes. MSEM can be applied to different hierarchical data structures quite commonly found in educational research, e.g., students nested in classrooms, or time-points nested in students.

In the first session we introduce multilevel modelling using manifest indicators, comparison of notation in MLM and MSEM, and model specification in the SEM framework.

In the second session we specify latent constructs for intraindividual data (time-points nested in students) and include level-specific predictors. We specify fixed and random effects models assuming “individuals as their own controls” type of models, in which the time perspective is not specified (Malmberg, 2020).

In the third session we apply Dynamic SEM assuming stationarity (no mean trends over time), specifying equidistant time-lags for lagged variables in diary data (a working-life dairy for a year). These time-series like models can be specified using the Bayesian estimators, allowing us to investigate within-person variability.

Contents 

Video-clip 1: Introduction to multilevel modelling in SEM, multilevel factor structures

Video-clip 2: Intraindividual SEM

Video-clip 3: Dynamic SEM

Friday 12 May 

09.00-09.30 Recap of multilevel SEM (questions can be posted in the Q&A document)

09:30-10:30 Work on MSEM and ISEM

10.30-10.45 Break

10.45-12.00 Work on DSEM

Software: We will mainly use the Mplus software (full version, input and output files are available, demo (https://www.statmodel.com/demo.shtml). Some parallel code for plotting is available in R (Lavaan). Materials are made available in advance of the session, and can also be used for self-study.

 

Week 5 Trinity Term

Mon 22/5 to Fri 26/5, 9-12 in Sem Room D

Advanced models in R (Lars Malmberg 9-12, 22-26/5/2023): Up to seven departmental Masters and Doctoral students can audit the lecture part of the course (each morning 22-26/5). Participants will be selected based on closeness between own research and the course contents.

In this course we will introduce relevant packages in R for regression models. We will use both existing secondary data and simulated data for learning key concepts for specifying models and interpreting findings.

Mon 22/5, 9-12 (The regression model) 

We start with an overview of multivariate statistics. Introduction to descriptive statistics and regression modelling for continuous dependent variables, using R. We will cover basic concepts: model, notation(s), estimation techniques and visual inspections. We will inspect continuous and dummy-coded predictors, inspect residuals and other indices of model-health.

Tue 23/5, 9-12 (Expansions of the regression model) 

We will expand the regression models to examples of interaction-effects, moderation models, and mediation models, also using path-analyses in R Lavaan. Link-functions for logistic regression (for binary outcomes) and probit regression (for ordinal data) are presented.

Wed 24/5, 9-12 (Introduction to path-analysis and structural equation modelling) 

Introduction to path-models and measurement models in R Lavaan. We will specify measurement models for continuous indicators of latent constructs, as well as measurement models for dichotomous indicators (0 = incorrect, 1 = correct) as indicators of latent constructs, analogous to IRT models.

Thurs 25/5, 9-12 (Multilevel regression) 

We will expand the regression models to multilevel regression analysis for hierarchically nested data, starting with students nested in classrooms in R lmer and Lavaan. We will cover fixed, random and contextual effects, and learn how to visualise findings.  

Fri 26/5, 9-12 (Advanced multilevel regression) 

We will expand the multilevel regression model to include other hierarchical data-structures: time-points nested in persons, test-items nested in assessors, specifying these as growth models, multivariate models and multiple membership models.