Model Estimation and Analysis: Linear Regression Models
Least squares regression
- Least squares
- Instrumental variables and 2SLS
- Least absolute deviations with bootstrapped standard errors
- Forward stepwise regression
- Extreme accuracy
- Condition number and variance inflation factors
- Leverage values
Summary statistics
- Fit measures, F, R2, adjusted R2, sum of squares
- Information criteria
- Likelihood function
- Durbin-Watson
- Condition number for data matrix
Predictions and residuals
- List, plot, retain
- Standardized residuals
- Influence analysis, leverage values, diagonals of ‘hat’ matrix
- Confidence interval for predictions
- Fill missing values
Robust estimation
- White and heteroscedasticity adjusted covariance matrix
- Newey-West estimator
- Cluster corrected covariance matrix
- Least absolute deviations - bootstrapped covariance matrix
- Nonparametric kernel density regression
Panel data
- Analysis of variance and covariance
- Fixed effects
- Random effects
- Random parameters (GLS, hierarchical)
- Balanced or unbalanced panels
- Autocorrelation correction
- Heteroscedasticity and autocorrelation tests
- LM and Hausman tests for effects
- White and Newey-West robust estimators
- Dynamic linear models (Arellano/Bond)
Heteroscedasticity
- Weighted least squares
- Multiplicative heteroscedasticity, maximum likelihood
- Goldfeld-Quandt, Breusch-Pagan tests
- Groupwise heteroscedasticity
- Heteroscedastic fixed and random effects
- ARCH, GARCH, GARCH in mean
Specification tests
- CUSUM
- Omitted variables
- Structural change
- J, Cox, PE tests
Restrictions
- F and Wald tests for linear restrictions
- Restricted regression
- Inequality restricted regression
- Wald tests for nonlinear restrictions
- Lagrange multiplier, likelihood ratio tests
Autocorrelation
- Durbin-Watson, Godfrey tests
- ML, Prais-Winsten, Cochrane-Orcutt, Hildreth-Lu estimators
- Hatanaka estimator for lagged dependent variable, 2SLS
- Higher order autoregressive
Systems of linear equations
- 2SLS
- 3SLS
- Seemingly unrelated regressions
- Autocorrelation
- Heteroscedasticity
- Singular equation systems with constraints
- GLS and maximum likelihood
- Cross and within equation constraints
- Covariance structures
- OLS, GLS
- Panel corrected standard errors
- Grouping of observation units
- Autocorrelation
Example
Linear regression of Household Income on Age, Eduction and Marital Status for women with a residual plot.
+----------------------------------------------------+ | Ordinary least squares regression | | Model was estimated Feb 26, 2007 at 11:40:30AM | | LHS=HHNINC Mean = .3374391 | | Standard deviation = .1582045 | | WTS=none Number of observs. = 2625 | | Model size Parameters = 4 | | Degrees of freedom = 2621 | | Residuals Sum of squares = 58.02916 | | Standard error of e = .1487954 | | Fit R-squared = .1164220 | | Adjusted R-squared = .1154106 | | Model test F[ 3, 2621] (prob) = 115.12 (.0000) | | Diagnostic Log likelihood = 1278.393 | | Restricted(b=0) = 1115.937 | | Chi-sq [ 3] (prob) = 324.91 (.0000) | | Info criter. LogAmemiya Prd. Crt. = -3.808843 | | Akaike Info. Criter. = -3.808843 | | Autocorrel Durbin-Watson Stat. = 1.0247658 | | Rho = cor[e,e(-1)] = .4876171 | +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ Constant| -.04835445 .02662990 -1.816 .0694 AGE | .00180144 .00034102 5.282 .0000 45.8411429 EDUC | .02087183 .00169078 12.345 .0000 10.3082433 MARRIED | .10791838 .00751798 14.355 .0000 .81600000
