Table 1.
Comparison of Coefficient Estimates, Marginal Effects, and Odds Ratios for the Linear Probability, Logit, and Probit Models for Two Different Model Specifications
| Variables | LPM | Logit | Probit | |||
|---|---|---|---|---|---|---|
| Simple | Full | Simple | Full | Simple | Full | |
| Constant | ||||||
| β/σ | 0.5062 (0.0063) | 0.5039 (0.0044) | 0.032 (0.032) | 0.109 (0.062) | 0.020 (0.019) | 0.057 (0.034) |
| x d | ||||||
| β/σ | 0.0478 (0.0089) | 0.0485 (0.0064) | 0.244 (0.045) | 0.827 (0.087) | 0.145 (0.027) | 0.468 (0.048) |
| IE | 0.0482 | 0.0459 | 0.0476 | 0.0465 | ||
| OR | 1.276 | 2.285 | ||||
| x 1 | ||||||
| β/σ | 0.1081 (0.0043) | 0.1037 (0.0032) | 0.551 (0.024) | 1.8424 (0.059) | 0.331 (0.014) | 1.033 (0.031) |
| ME | 0.1085 | 0.1021 | 0.1084 | 0.1024 | ||
| OR | 1.734 | 6.312 | ||||
| x 2 | ||||||
| β/σ | 0.1968 (0.0037) | 0.2014 (0.0031) | 1.000 (0.026) | 3.655 (0.089) | 0.603 (0.015) | 2.046 (0.048) |
| ME | 0.1972 | 0.2025 | 0.1977 | 0.2027 | ||
| OR | 2.719 | 38.66 | ||||
| x 3 | ||||||
| β/σ | 0.0963 (0.0032) | 1.678 (0.058) | 0.938 (0.031) | |||
| x 4 | ||||||
| β/σ | 0.2959 (0.0030) | 5.40 (0.12) | 3.018 (0.066) | |||
| RMSE | 0.45 | 0.32 | ||||
| R 2 | 0.20 | 0.59 | ||||
| Pseudo R 2 | 0.17 | 0.74 | 0.17 | 0.74 | ||
Notes. Robust standard errors are in parentheses. 10,000 observations of simulated data, based on the formula for the underlying latent dependent variable: y* = 0.5x d + x 1+2x 2 + x 3+ 3x 4 with covariates normally distributed, except x d which is a dummy variable.
IE, incremental effect; ME, marginal effect; OR, odds ratio; RMSE, root mean squared error.