# Interaction Design Based on Big Data Community Home Care Service Demand Levels
## 2 Big Data Community Home Care Service Demand Hierarchy
### Service Requirements Hierarchy  
#### 2.2.1 Demand Influencing Factors  
Based on the community big data formed by the survey results of the elderly at home group, the structural model and the measurement model are fused and a multi-indicator, multi-factor model is established to analyze the influencing factors of the service demand by analyzing the cause variables, latent variable paths, and indicator variables, in order to comprehensively measure the objective values of latent variables and accurately classify the  
Figure 1: Community aging-in-place big data. demand levels. Assuming that the demand for educational services is \(\eta\) (i.e., latent variable) and the basic information parameters such as health status, self-care ability, and economic level of the elderly population are \(x_{q}\) (i.e., cause variables), the equation expressions of the structural model in the model is:  
\[\eta=\gamma_{1}\chi_{1}+\gamma_{2}\chi_{2}+\ldots+\gamma_{q}\chi_{q}+\xi \tag{1}\]  
In the above equation, \(\xi\) is the error term and is used as a compensation parameter. Assuming that the demand for the four services is \(y_{p}\) (i.e., the indicator variable) and the error term is \(\varepsilon_{P}\), the equation expression for the measurement model in the model is :  
\[y_{1}=\lambda_{1}\eta+\varepsilon_{1} \tag{2}\]  
\[y_{p}=\lambda_{p}\eta+\varepsilon_{p} \tag{3}\]  
The measurement model reflects a linear relationship between the demand for educational services and the demand for four services, including life care. After simplification, a simplified equation of the two models is obtained. It is as follows:  
\[\eta=\gamma^{\prime}x^{\prime}+\xi \tag{4}\]  
\[y^{\prime}=\lambda^{\prime}\eta+\varepsilon^{\prime} \tag{5}\]  
where \(x^{\prime}=\big{(}x_{1},x_{2},\ldots,x_{q}\big{)}\) and \(y^{\prime}=(y_{1},y_{2},\ldots,y_{p})\) are the sets of variablesof observable exogenous causes and endogenous indicators, and \(\gamma^{\prime}=\big{(}\gamma_{1},\gamma_{2},\ldots,\gamma_{q}\big{)}\) and \(\lambda^{\prime}=\big{(}\lambda_{1},\lambda_{2},\ldots,\lambda_{p}\big{)}\) are the sets of structural parameters of the structural and measurement models. All other parameters are error terms. The simplified two-model defining equations after the union are obtained are:  
\[y=\Pi x+v \tag{6}\]  
Among them. \[v=\lambda^{\prime}\xi+\varepsilon \tag{7}\]  
\[\Pi=\gamma\lambda^{\prime} \tag{8}\]  
The measurement errors are assumed to be normally distributed and independent of each other in the above set of equations, expressed as [19; 20; 21]:  
\[E=(\xi)=E(\varepsilon)=0 \tag{9}\]  
\[\eta=\gamma_{1}\chi_{1}+\gamma_{2}\chi_{2}+\ldots+\gamma_{q}\chi_{q}+\xi \tag{1}\]0  
\[\eta=\gamma_{1}\chi_{1}+\gamma_{2}\chi_{2}+\ldots+\gamma_{q}\chi_{q}+\xi \tag{1}\]1  
\[\eta=\gamma_{1}\chi_{1}+\gamma_{2}\chi_{2}+\ldots+\gamma_{q}\chi_{q}+\xi \tag{1}\]2  
The model focuses on the calculation of the function matrix through the covariance matrix. In this case, the covariance matrix consists of observable variables and the function matrix consists of parameters to be estimated. After substituting the observable variables, the overall covariance \(\Sigma(\theta)\) is solved by using the following equation:  
\[\eta=\gamma_{1}\chi_{1}+\gamma_{2}\chi_{2}+\ldots+\gamma_{q}\chi_{q}+\xi \tag{1}\]3  
The overall covariance \(\Sigma(\theta)\) in the above equation is the covariance matrix consisting of the observable variables. The parameter to be estimated exists in the vector \(\theta\). This vector can be solved by the structural model equation and the measurement structural model equation. It is combined with the structural model equation to obtain the value of the demand for educational services, i.e., the value of the latent variable. In the parameter estimation of the structural model equation, there are usually two cases that require the use of different methods to accomplish. The parameter estimation methods for the different cases are described in detail as follows.