China’s economic and social development and transformation have led to changes in the mental health of the nation, in which changes in family structure brought about by social transformation have become an important factor affecting the nation’s mental health. This paper utilizes the logistic regression model in the multivariate classification analysis tool to explore the causal relationship between social support and mental health. Social support is divided into three levels: life support, economic support, and emotional support, and the impact of social holding on the mental health of the elderly is empirically analyzed. Based on the logistic regression model, the least squares estimation method was used to obtain the degree of influence of social support on the mental health of the elderly. Analyzing the degree of mental health of the sample, the total score of the elderly over 80 years old is lower, and the mean and standard deviation are 3.248 and 0.574, respectively, indicating that there is a certain downward trend in the mental health of the elderly of high age. Relative to men, emotional support has a more significant effect on the depression level of female elderly, with a regression coefficient of -0.059, P<0.05. Based on the findings of the study, five relevant recommendations are proposed to further enhance the mental health of the nation, such as providing good mental health services for the elderly, and actively creating a livable environment for the elderly.
