# A General Solution for the Errors in Variables (EIV) Model with Equality and Inequality Constraints
## 4 Experiment Analysis
### Experiment with Both Equality and Inequality Constraints  
Data of the third example using equality and inequality constraints come from [PERSON] and [PERSON] [19]. The coefficient matrix \(\mathbf{A}\), observation vector \(\mathbf{L}\), constraints matrix \(\mathbf{G}_{2}\) and constraints constant vector \(W_{2}\) are located in Table 4.  
\begin{table}
\begin{tabular}{c c c c} \hline  & \(\mathbf{A}\) & & \(\mathbf{L}\) \\ \hline
0.9501 & 0.7620 & 0.6153 & 0.4057 & 0.0578 \\
0.2311 & 0.4564 & 0.7919 & 0.9354 & 0.3528 \\
0.6068 & 0.0185 & 0.9218 & 0.9169 & 0.8131 \\
0.4859 & 0.8214 & 0.7382 & 0.4102 & 0.0098 \\
0.8912 & 0.4447 & 0.1762 & 0.8936 & 0.1388 \\ \hline  & \(\mathbf{G_{2}}\) & & & \(W_{2}\) \\ \hline
0.2027 & 0.2721 & 0.7467 & 0.4659 & 0.5251 \\
0.1987 & 0.1988 & 0.4450 & 0.4186 & 0.2026 \\
0.6037 & 0.0152 & 0.9318 & 0.8462 & 0.6721 \\ \(-0.1\leq x_{i}\leq 2.0\), \(i=1,2,3,4\) & & & \\ \hline \end{tabular}
\end{table}
Table 4: Data from [PERSON] et al. (2013) [21].  
\begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{A}\) & \(\mathbf{L}\) & \(\mathbf{G_{2}}\) & \(\mathbf{W_{2}}\) \\ \hline
1 & \(-39.7312\) & \(-18.6749\) & \(-1\) & 0 & \(-1.9500\) \\
1 & \(-29.0831\) & \(-11.4825\) & 1 & 0 & \(2.0500\) \\
1 & \(-21.1294\) & \(-7.6373\) & 0 & \(-1\) & \(-0.4500\) \\
1 & \(-9.5689\) & \(-3.0315\) & 0 & 1 & \(0.5500\) \\
1 & \(0.1594\) & \(2.3574\) & \(-2\) & 1 & \(-3.4500\) \\
1 & \(9.3462\) & \(6.8975\) & 2 & \(-1\) & \(3.5500\) \\
1 & \(19.7832\) & \(11.9379\) & & & \\
1 & \(30.1713\) & \(17.7448\) & & & \\
1 & \(41.7892\) & \(22.7045\) & & & \\
1 & \(51.3847\) & \(27.7086\) & & & \\ \hline \end{tabular}
\end{table}
Table 2: Data set and inequality constraints of the regression model.  
The inequality constrained equation can be expressed as  
\[\left[\mathbf{G}_{2}^{\mathbf{T}}\qquad\mathbf{I}_{4}\otimes[1-1]\right]^{\mathbf{T}}\mathbf{X}\leq \left[\mathbf{W}_{2}^{\mathbf{T}}\qquad\mathbf{I}_{4}\otimes[0.1\;2]\right]^{\mathbf{T}}\]  
Equality constraints: \(\left[-2\quad 1\quad 3\quad 0\right]\mathbf{X}=2\).  
Table 5 presents the adjustment results in three different methods: (1) only inequality constraints are considered by using the Fang algorithm presented by [PERSON] and [PERSON] (2016), IC-Fang; (2) only inequality constraints are considered by using our general solution, IC-EIV; (3) equations and inequality constraints are considered simultaneously by using our general solution, EIC-EIV; and (4) the Fang algorithm presented byFang and [PERSON] [19], EIC-Fang.  
From Table 5, we can estimate that the parameter estimates of considering inequality constraints only is different from that of considering both equality and inequality constraints. The results of our general solution are identical to those presented in [PERSON] and [PERSON] [19]. It discloses the feasibility of our general solution. It is obvious that the TSSR of EIC-EIV and EIC-Fang are larger than that of IC-EIV and IC-Fang, which is due to the newly added equality constraint. However, the precision of the parameter estimates is improved [19]. It is worth noting that different results of precision for the parameter estimates are shown in two appraisal approaches.