G89 2247 Structural Equation Models Overview of course Setting time for lab session Statistical thinking about causality SEM as Causal Models Matrix Algebra Tools G89 2247 Lecture 1 1 Goals of Course Introduce you to basic concepts and techniques of structural equation models Help you develop a critical perspective regarding what is and is not learned using SEM Provide skills for your continued self education Provide a context for you to apply SEM methods to a sophisticated problem of your own choosing G89 2247 Lecture 1 2 What are Structural Equation Models Systems of linear equations that describe a network of relations among variables Structural not simply predictive relations Implied systems of nonlinear equations that describe patterns of variances and covariances among variables Output of software systems such as LISREL EQS AMOS and MPlus G89 2247 Lecture 1 3 Why are SEM methods useful Hoyle s 1994 review tells us that SEM can address Questions about causal process Basic questions of measurement Questions about causal process when variables are not well measured SEM methods share most of the strengths of OLS multiple regression SEM models can be used to impress your family friends and colleagues if not reviewers and editors G89 2247 Lecture 1 4 An example of a structural equation model Stress Distress Extreme stress is known to lead to psychological breakdown Battle fatigue PTSD Severe stress is believed to cause depression anxiety disorder psychosis Stress Distress1 Distress2 G89 2247 Lecture 1 5 Stress causes distress and psychopathology To what extent is this common belief true How much stress is needed to cause distress For a unit change in stress how much do we expect distress to increase How do we account for the many persons who experience stress who manage to function without psychopathology Is the purported causal process universal or does it operate only in a subset of the population G89 2247 Lecture 1 6 Causal Inference Issues Causal inference is often illusive in social and behavioral sciences Prototypes of Causal Effects seem to implicate primary single causes billiard balls bacteria or viruses In reality effects usually have multiple causes For distress Stressors Personal dispositions Familial factors Social environment Biological environment G89 2247 Lecture 1 7 Causal Inference continued Effects of causes are not always constant social buffers developmental stages immune system interventions synergistic causal effects stochastic variation in causal factor strength stochastic measurement factors G89 2247 Lecture 1 8 David Hume s framework for Causality If E is said to be the effect of C then 1 C and E must have temporal and spatial contiguity ASSOCIATION 2 C must precede E temporally DIRECTION 3 There must be CONSTANT CONJUNCTION If C then E for all situations G89 2247 Lecture 1 9 Although still influential Hume s analysis is known to have limitations Analysis of any cause C must be isolated from competing causes ISOLATION Constant conjunction is too restrictive stochastic processes affect causal relations and mechanisms may vary across situations Causal relations may be expressed in terms of expectations over stochastic variation G89 2247 Lecture 1 10 Formal causal analyses have led to important advances Robert Koch the Nobel Prize winning bacteriologist investigated bacteria as causes of disease using three principles The organism must be found in all cases of the disease in question association The organism must be isolated and grown in pure culture isolation When inoculated with the isolated organism susceptible subjects must reproduce the disease direction and hedged constant conjunction G89 2247 Lecture 1 11 Causal Process in Time In the behavioral social and biological sciences the units of observation cannot be trusted to stay the same over time For example in Koch s inoculation test how do we know that the subject had not been infected by chance For studies of distress we expect both stress and distress to change over time G89 2247 Lecture 1 12 Statisticians developed the randomized experiment to address causal issues Randomly assign subjects to one of two conditions Treatment T or Control C Administer treatment and control procedures Measure outcome variable Y assumed to reflect the process of interest blind to treatment group Infer effect of treatment from difference in group means G89 2247 Lecture 1 13 Holland s formal analysis of randomized experiments Suppose Y u is a measurement on subject u that reflects the process that is supposed to be affected by treatment T If subject u is given treatment T then YT u is observed If subject u is given a control treatment C then Y C u is observed We would like to compare YT u with YC u but only one of these can be available as u is either in T or C Let the desired comparison be called D Y T u YC u Holland calls this the Effect of cause T Although D can not be observed its average can be estimated by computing D YT YC G89 2247 Lecture 1 14 Between subject is substituted for within subject information Within subject analyses are intuitively appealing but require strong assumptions about constancy over time When D 0 then ASSOCIATION is established Randomization prior to treatment deals with the causal issue of DIRECTION It also partially supports ISOLATION double blind trials manipulation checks help address other aspects of isolation Randomization does not establish CONSTANT CONJUNCTION The effect is only established for the specific experimental conditions used in the study G89 2247 Lecture 1 15 Key Feature Treatment is applied to subjects sampled into group T Holland argues that this manipulation is critical to guarantee DIRECTION and ISOLATION Holland and Rubin go on to assert that clear causal inference is only possible if manipulation is at least conceivable They propose the motto NO CAUSATION WITHOUT MANIPULATION G89 2247 Lecture 1 16 NO CAUSATION WITHOUT MANIPULATION This motto is not popular with sociologists and economists It explicitly denies causal status to personal attributes such as race sex age nationality and family history Instead it encourages the investigation of processes such as discrimination physical changes corresponding to age government policy and biochemical consequences of genetic makeup G89 2247 Lecture 1 17 NO CAUSATION WITHOUT MANIPULATION To illustrate Holland would not say that my height causes me to hit my head going into my suburban cellar as my height cannot be