2.2.1 理论公式输出

X <- c(paste0(rep(c("X","Z"),each=4),1:4), "fathedu", "mothedu")
Y <- "lwage"
Greek.g <- c("alpha","beta","lambda")
Greek.n <- c(4,4,2)
#type <- "srm"
Obs <- "i"
N.row <- 4
Cst <- F

总体回归模型PRM：

\[\begin{equation} \begin{alignedat}{999} lwage_i&=&&\alpha_{1}X1_i+&&\alpha_{2}X2_i+&&\alpha_{3}X3_i+&&\alpha_{4}X4_i\\&+&&\beta_{1}Z1_i+&&\beta_{2}Z2_i+&&\beta_{3}Z3_i+&&\beta_{4}Z4_i\\&+&&\lambda_{1}fathedu_i+&&\lambda_{2}mothedu_i+&&u_i \end{alignedat} \tag{2.1} \end{equation}\]

样本回归模型SRM：

srm_test <- lx.psm(x =X, y = Y, greek.g = Greek.g, greek.n = Greek.n,
       type = "srm", intercept = Cst, lm.label = "srm", 
       obs = Obs, n.row = N.row)

\[\begin{equation} \begin{alignedat}{999} lwage_i&=&&\hat{\alpha}_{1}X1_i+&&\hat{\alpha}_{2}X2_i+&&\hat{\alpha}_{3}X3_i+&&\hat{\alpha}_{4}X4_i\\&+&&\hat{\beta}_{1}Z1_i+&&\hat{\beta}_{2}Z2_i+&&\hat{\beta}_{3}Z3_i+&&\hat{\beta}_{4}Z4_i\\&+&&\hat{\lambda}_{1}fathedu_i+&&\hat{\lambda}_{2}mothedu_i+&&e_i \end{alignedat} \tag{2.2} \end{equation}\]

样本回归函数SRF：

srf_test <- lx.psm(x =X, y = Y,greek.g = Greek.g, greek.n = Greek.n,
       type = "srf", intercept = Cst, lm.label = "srf",
       obs = Obs, n.row = N.row )

\[\begin{equation} \begin{alignedat}{999} \widehat{lwage}_i&=&&\hat{\alpha}_{1}X1_i+&&\hat{\alpha}_{2}X2_i+&&\hat{\alpha}_{3}X3_i+&&\hat{\alpha}_{4}X4_i\\&+&&\hat{\beta}_{1}Z1_i+&&\hat{\beta}_{2}Z2_i+&&\hat{\beta}_{3}Z3_i+&&\hat{\beta}_{4}Z4_i\\&+&&\hat{\lambda}_{1}fathedu_i+&&\hat{\lambda}_{2}mothedu_i \end{alignedat} \tag{2.3} \end{equation}\]

2.2.2 数值公式输出

require("wooldridge")
mroz <- wooldridge::mroz %>%
  as_tibble() %>%
  select(lwage, educ,exper, 
         fatheduc,motheduc,everything()) %>%
  filter(!is.na(wage))

mod_origin <- formula(lwage ~ educ + nwifeinc +exper+I(exper^2) + I(exper^2*city)  )

ols_origin <- lm(formula = mod_origin, data = mroz)

默认形式：

lx_out<- lx.est(lm.mod = mod_origin, lm.dt = mroz)

\[\begin{alignedat}{999} \widehat{lwage}&=&&-0.53&&+0.10educ_i&&+0.01nwifeinc_i\\&(s)&&0.2011&&0.0148&&0.0032\\&(t)&&-2.61&&+6.67&&+1.59\\&(cont.)&&+0.04exper_i&&-0.00exper^2_i&&+0.00exper^2*city_i\\&(s)&&0.0132&&0.0004&&0.0002\\&(t)&&+3.23&&-2.19&&+0.79 \end{alignedat}\]

srm形式：

lx_out<- lx.est(lm.mod = mod_origin, lm.dt = mroz, style = "srm")

\[\begin{alignedat}{999} {lwage}&=&&-0.53&&+0.10educ_i&&+0.01nwifeinc_i\\&(s)&&0.2011&&0.0148&&0.0032\\&(t)&&-2.61&&+6.67&&+1.59\\&(cont.)&&+0.04exper_i&&-0.00exper^2_i&&+0.00exper^2*city_i&&+e_i\\&(s)&&0.0132&&0.0004&&0.0002\\&(t)&&+3.23&&-2.19&&+0.79 \end{alignedat}\]

一行形式：

lx_out<- lx.est(lm.mod = mod_origin, lm.dt = mroz, style = "srm", opt = c("p"))

\[\begin{alignedat}{999} {lwage}&=&&-0.53&&+0.10educ_i&&+0.01nwifeinc_i\\&(p)&&0.0093&&0.0000&&0.1116\\&(cont.)&&+0.04exper_i&&-0.00exper^2_i&&+0.00exper^2*city_i&&+e_i\\&(p)&&0.0014&&0.0288&&0.4322 \end{alignedat}\]