Model Estimation & Data Analysis: Linear Regression Models
LIMDEP and NLOGIT software offer a complete set of powerful tools for linear regression estimation, hypothesis testing, specification analysis and simulation.
Least squares regression
- Least squares
- Instrumental variables and 2SLS
- Least absolute deviations with bootstrapped standard errors
- Extreme accuracy
Summary Statistics
- Fit measures, F, R2, adjusted R2, sum of squares
- Information criteria
- Likelihood function
- Durbin-Watson
Predictions and Residuals
- List, plot, retain
- Standardized residuals
- Confidence interval for predictions
- Impute missing values
Robust Estimation
- White and heteroscedasticity adjusted covariance matrix
- Newey-West estimator
- Cluster corrected covariance matrix
- Kernel density regression
Panel Data
- Analysis of variance and covariance
- Fixed effects
- Random effects
- Random parameters (GLS, hierarchical)
- Balanced or unbalanced panels
- Cluster 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
- 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
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
Linear Regression Example
Linear regression of Household Income on Age, Eduction and Marital Status for women with a residual plot.
----------------------------------------------------------------------------- Ordinary least squares regression ............ LHS=HHNINC Mean = .34489 Standard deviation = .16279 No. of observations = 1000 Degrees of freedom Regression Sum of Squares = 4.58257 3 Residual Sum of Squares = 21.8912 996 Total Sum of Squares = 26.4738 999 Standard error of e = .14825 Fit R-squared = .17310 R-bar squared = .17061 Model test F[ 3, 996] = 69.49881 Prob F > F* = .00000 Diagnostic Log likelihood = 491.89637 Akaike I.C. = -3.81367 Restricted (b=0) = 396.86157 Bayes I.C. = -3.79404 Chi squared [ 3] = 190.06961 Prob C2 > C2* = .00000 --------+-------------------------------------------------------------------- | Standard Prob. 95% Confidence HHNINC| Coefficient Error z |z|>Z* Interval --------+-------------------------------------------------------------------- Constant| -.04595 .03469 -1.32 .1854 -.11394 .02205 AGE| .00054 .00046 1.16 .2474 -.00037 .00145 EDUC| .02379*** .00198 11.99 .0000 .01990 .02767 MARRIED| .11794*** .01193 9.88 .0000 .09455 .14133 --------+-------------------------------------------------------------------- Note: ***, **, * ==> Significance at 1%, 5%, 10% level. -----------------------------------------------------------------------------