Met 2212 Multivartate Statistics HoTesting OLSregression LISREL IS

Met 2212 - Multivartate Statistics Ho-Testing OLS-regression LISREL IS GREEK TO ME The SEM model LISREL SOFTWARE Ulf H. Olsson Professor of Statistics

THE LISREL MODEL Ulf H. Olsson

THE LISREL MODEL Branch Loan Satisfaction Loyalty Savings Ulf H. Olsson

THE LISREL MODEL Ulf H. Olsson

THE LISREL MODEL (Factor Model) Ulf H. Olsson

THE LISREL MODEL (Factor Model) Ulf H. Olsson

THE LISREL MODEL Ulf H. Olsson

THE LISREL MODEL Ulf H. Olsson

THE LISREL MODEL Ulf H. Olsson

Greek Letters CAP / low er Name & Description • C A P ALPHA (AL-fuh) First letter of the Greek alphabet. / l BETA (BAY-tuh) o w e GAMMA (GAM-uh) r • N a DELTA (DEL-tuh) m e EPSILON (EP-sil-on) The second form of the lower case epsilon is used as the “set membership” symbol. & D e Ulf H. Olsson s c

Greek Letters ZETA (ZAY-tuh) ETA (AY-tuh) THETA (THAY-tuh) IOTA (eye-OH-tuh) KAPPA (KAP-uh) Ulf H. Olsson

Greek Letters LAMBDA (LAM-duh) MU (MYOO) NU (NOO) XI (KS-EYE) OMICRON (OM-i-KRON) Rarely used because it looks like an ‘o. ’ Ulf H. Olsson

Greek Letters PI (PIE) RHO (ROW) SIGMA (SIG-muh) TAU (TAU) Ulf H. Olsson

Greek Letters UPSILON (OOP-si-LON) PHI (FEE) The two versions of lower-case Phi are used interchangeably. CHI (K-EYE) PSI (SIGH) OMEGA (oh-MAY-guh) Last letter of the Greek alphabet. Ulf H. Olsson

Parameter Function Ulf H. Olsson

Multivariate Normal Distribution Ulf H. Olsson

The Maximum Likelihood Estimator Ulf H. Olsson

Measurement Error in Linear Multiple Regression Models • Ulf H Olsson • Professor Dep. Of Economics

The stadard linear multiple regression Model Ulf H. Olsson

Measurement Error/Errors-in-variables Ulf H. Olsson

The consequences of neglecting the measurent error Ulf H. Olsson

The consequences of neglecting the measurent error • The probability limits of the two estimators when there is measurement error present: • The disturbance term shares a stochastic term (V) with the regressor matrix • => u is correlated with X and hence E(u|X) 0 Ulf H. Olsson

The consequences of neglecting the measurent error • Lack of orthogonality – crucial assumption underlying the use of OLS is violated ! Ulf H. Olsson

The consequences of neglecting the measurent error • The inconsistency of b Ulf H. Olsson

The consequences of neglecting the measurent error • The inconsistency of b Ulf H. Olsson

The consequences of neglecting the measurent error • The inconsistency of b • Bias towards zero (attenuation) for g=1 • In multiple regression context things are less clear cut. Not all estimates are necessarilly biased towards zero, but there is an overall attenuation effect. Ulf H. Olsson

The consequences of neglecting the measurent error • In the limit we find: Ulf H. Olsson

The consequences of neglecting the measurent error • The estimator is biased upward Ulf H. Olsson

The consequences of neglecting the measurent error Ulf H. Olsson

The consequences of neglecting the measurent error Ulf H. Olsson