According to the causal inference problem under the counter-factual framework an L2 factor analysis method from the perspective of factor analysis and optimization is proposed to estimate counter-factual value and L1 loss function is introduced to optimize L1 risk. Combining causal inference with orthogonal factor model the counter-factual value which is supposed to estimate is regarded as missing value transforming the counter-factual value estimation of causal inference into latent factor model estimation with missing value. Discarding the missing value in the panel data the latent results and mean treatment effect are derived directly by optimization and therefore avoid the loss of information using L1 factor analysis instead of L2 factor analysis to estimate the model making robustness improvements and obtaining the median treatment effect. Alternate convex programming is introduced to minimize the objective function in the L1 and L2 factor analysis and its implementation steps are given. Empirical study based on the case of tobacco policy in California is made to compare L1 L2 factor analysis and other causal inference methods. The results show that the L1 and L2 factor estimator is also applicable to the prediction of macroeconomic variables. Finally by setting up pseudo-treat unit assumption and pseudo-time assumption respectively it has been verified that L1 has more robust prediction effect than other methods.