Statistical Modelling Dr. Yang Hu yang.hu@Lancaster.ac.uk Dr. Stuart Bedston s.bedston@lancaster.ac.uk
Overview of the day Session 1: Introduction to statistical modelling Session 2: Dependent variables, independent variables, and distributions Session 3: From variables to models: Model choice, fitting and interpretation Session 4: Fitting models: diagnostics and further cautions Session 5: Building models: Mediation and moderation analysis Session 6: Advanced modelling techniques and learning resources
Introduction to Statistical Modelling Dr. Yang Hu yang.hu@Lancaster.ac.uk Dr. Stuart Bedston s.bedston@lancaster.ac.uk
Session overview Practice and example dataset for the day Inferential statistics: What is it? How is it different from descriptive statistics? Why and when to use statistical modelling? Workflow of statistical modelling
Example dataset British Crime Survey unrestricted teaching dataset 2007–2008 (see www.crimesurvey.co.uk for more information on the BCS) 11,676 random respondents (~25%) out of the 46,983 respondents who answered the follow-up Module B. 35 variables covering different types/substantive topics Download the teaching dataset: https://discover.ukdataservice.ac.uk/Catalogue/?sn=6891&type=Data%20catalogue)
Inferential statistics: What is it? Inferential statistics: Inferential statistics are techniques that allow us to use sample data to make generalizations about the populations from which the samples were drawn. Descriptive statistics: Analysis that helps describe, show or summarise data. Descriptive statistics do not allow us to make conclusions beyond the data.
Inferential statistics: What is it? Identify and extract underlying rules/regularities of relationships between different factors/ variables
From descriptive to inferential statistics From description of statistical “reality” to the generalization of underlying “rules”. Example: age and worry of being victim of personal crime (N = 8,434) Variable Mean (Median) Range SD Skewness Kurtosis Age 50.42 (49) 16 to 101 18.54 .11 2.10 Level of worry about being victim of personal crime .46 (–.12) –1.70 to 2.85 1.00 .83 3.54
From descriptive to inferential statistics Descriptive statistics (continued)
From descriptive to inferential statistics Descriptive statistics (continued) Each dot represents an observed data point Bivariate correlation: –.066
From descriptive to inferential statistics Descriptive statistics (continued) Summarised statistics by cohort group
From descriptive to inferential statistics Inferential statistical modelling (Ordinary least squares linear regression—to be covered in Session 4)
From descriptive to inferential statistics Inferential statistical modelling (Predictive margin with 95% confidence intervals) From descriptive observation to generalisable equation Worry=–.006*Age + .346
From descriptive to inferential statistics What if we also need to take account of multiple factors: gender, ethnicity, experience of crime in past 12 months, etc.
Why/when to use statistical modelling? Finding the underlying rules, patterns and regularities, instead of just describing the data. Such rules are transferrable—can be modified and used to predict and test hypothesis. The “fitness” of the rule can be assessed. Unravel complex/multivariate relationships (that cannot be easily summarised with descriptive statistics) Go beyond the dataset/sample to infer about a broader population Going beyond the past and present: predict future trends and (not yet known) outcomes Test hypothesis Assess the relative importance of predictors Assess the relationship between factors in determining the outcome :
Why/when to use statistical modelling? Why do we need multivariate analysis? To avoid omitted variable bias (get the most accurate estimates of the net role of a given variable) To get a more holistic understanding of the outcome of interest :
Workflow of statistical modelling Before Define concepts and measurements/variables—dependent and independent variables Clean and prepare variables During Devise research question/hypothesis, specifying “relationship (equation)” between variables (so usually 2+ variables) Fit models Build models After Diagnose models and statistical assumptions Report and interpret models