Generalised (Least Squares) Linear Model  or bivariate linear regression -  this is the simplest form is the bivariate linear regression, involving a straight line relationship between one response (dependent or regressor) variable and one predictor (independent or explanatory) variable.  

Multiple regression  -this extends the bivariate linear regression to include more than one predictor variable.

Linear Models for Categorical Data -  categorical data require special attention in regression analysis because, unlike dichotomous or continuous variables, they cannot by entered into the regression equation just as they are. Instead, they need to be recoded into a series of variables which can then be entered into the regression model.  Types of linear models:

•  Logit/logistic/multinomial logistic - used when the response variable is binary (rather than continuous).  Models how the logarithm of the odds of having a particular characteristic varies with the values of the predictor variables. 
•  Loglinear - this is used when we only have group level data and the data take the form of a contingency table.  The dependent variable is the number of cases in a cell of a table. 

Survival and Event History Analysis  - survival models are applied to data that specify the time elapsed until an event occurs. This concept of 'time elapsed' implies a starting event and a terminating event (e.g. birth and death, divorce and remarriage).  Survival times are the observed times from the initiation of a process of interest (e.g. birth) and the occurrence of the event of interest (e.g. death).  In practice, time is always measured in discrete units.  When discrete units are very small, time can be treated as if it were measured on a continuous scale.  When larger (months, years or decades), it is more appropriate to use discrete time methods).  Events consists of some qualitative change that occurs at a specific point in time and does not refer to a gradual change.  An event history is a longitudinal record of when events happened to a sample of individuals or collectives.  It's worth noting the term 'censoring' which means here as 'lost to observation'.  Left censoring is when the event happens prior to the observational period and right censoring when the subject has not had the event when the observational period is terminated. 

•  Life Tables  - this is a statistical presentation (table or spreadsheet) of the life history of a cohort, commencing with the starting event, as the cohort is progressively thinned out over time by failures (i.e. terminating events).  A life table is a basic building block for hazards models.   There are two ways for calculating a life table: (1) actuarial method and (2) product limit model (used in estimation of hazard models and is also known as the Kaplan-Meier life table; survival function is calculated at each unique failure time).  The actuarial method is often used by life insurance companies as they can show the probability of a person at a certain age dying before their next birthday (they are often called mortality tables).  These statistics calculate the remaining life expectancy for people at different ages and stages and the probability of surviving a particular year of age.  Actuarial life tables are computed separately for men and women as they have different mortality rates.  
•   Cox Proportional Hazards Regression - this could be viewed as multivariate life table where the hazard is a function of time and other specified predictor variables, such as residence and education. 
•  Kaplan-Meier Curve -  this is a visual representation that shows the probability of an event at a respective time interval.
•  Discrete Time Model - used to study the patterns and correlates of the occurrences of events (marriages, deaths, becoming unemployed etc). 

Multilevel models  - hierarchical regression analysis, designed to handle hierarchical and cluster data; looks at group effects on individuals when grouping is present. Types of models include: 

•  Hierarchical linear modelling
•  Random coefficients modelling (RC)
•  Covariance components models 

Multiple Classification Analysis (MCA) - related to multiple regression and is a technique for examining the interrelationship between several predictor variables and one dependent variable in the context of an additive model.  Best explained as multiple regression with dummy variables! Response variable is quantitative and predictive variables are categorical represented by dummy variables. 

Discriminant Function Analysis or Latent Class Analysis - related to logistic regression 

•  Cluster Analysis  - aim is the detection of patterns or indications of potentially interesting relationships in the data. Only when some pattern is thought to exist can the further steps be taken of setting up models and hypotheses for future investigation. The results are produced in the form of a graph or some other type of visual display.  
•  Factor Analysis & Covariance Structure Models (path analysis/LISREL models)  - two methods of testing latent models.  Latent variables are often theoretical concepts such as intelligence, which cannot be directly measured or cannot be measured without error.  We have to make measurements using variables that are assumed to be indicators of the concepts that we are interested in.   Factor analysis is a regression model for the observed variables on the unobserved latent variables or factors.  There are two types: Exploratory Factor Analysis where the detailed model rating the latent to the observed is not determined before the analysis and Confirmatory Factor Analysis where the number of latent variable is set by the analyst. 
•  Structural Equation Modelling  - these look at tentative casual relations between a set of latent dependent and latent independent variables.  

Causality 

•  Path Analysis  - can be seen as an extension of the ordinary regression model.  It analyses how a predictor variable affects the response variable not only directly but also indirectly through one or more intervening variables.  First step is to portray it in a diagram with arrows indicating direction of causality. 
•  Graphic Chain Modelling  - used to understand the causal structure underlying the dependence among variables.  Variables are grouped into response, intermediate and explanatory variables.  Intermediate variables can be treated as response to some variables and explanatory for others.  Arrows point from explanatory variables to response variables. 
• Worth noting that to establish causality, you need to be able to prove X came before Y (temporal priority of the independent variable), that the observed relationship between X and Y didn't happen by chance alone (non-spurious), and that there is nothing else that accounts for the X -> Y relationship (empirical association).   In epidemiology, people use the Bradford Hill Criteria to show casualty.   This consists of:
  • Strength
  • Consistency
  • Specificity
  • Temporality
  • Biological gradient
  • Coherence
  • Experimental evidence
  • Analogy
  • Plausibility