# Empirical Evidences for Urban Influences on Public Health in Hamburg
## 3 Results: Identifying Urban Influences on Health  
### Principal Component Analysis  
A principal component analysis (PCA) was conducted to obtain a data-based systematization of the variables and to inform the linear regression model (LR). It was ensured that all items correlated to the degree of at least 0.3 with at least one other item. The Kaiser-Meyer-Olkin measure of sampling adequacy is 0.84, therefore clearly above the commonly recommended value of 0.6. [PERSON]'s test of sphericity is significant (\(x^{2}\) (829) = 11,274.435, \(p<0.01\)). The diagonals of the anti-image correlation matrix are all over 0.5, and the communalities are all above 0.3, further confirming that each item shares some common variance with other items. Given these results, factor analysis was decided to be suitable with all 41 items selected. Initial eigenvalues for the first three components explained 19%, 9%, and 7% of the variance respectively, with eigenvalues of 3% to 7.7%. The fourth to 12 th factors had eigenvalues above one, and each explained 2.5% to 4.7% of the variance. Solutions for three to 12 factors were each examined using Quartimax rotation of the factor loading matrix. The nine-factor solution, which explained 59% of the variance, was preferred because of: (a) the goal of achieving a variance elucidation of \(>\)60% using the defined factors; (b) examination of the scree plot; and (c) the ninth factor was the last factor to explain more than 3% of the variance. No items were eliminated because all items contribute to a simple factor structure and meet a minimum criterion of having a primary factor loading of 0.37 or above. The factor loading matrix for this solution is presented in Table 2.  
The factor labels were deducted from the variables assigned to the factors. Internal consistency for each of the scales was examined using [PERSON]'s alpha. [PERSON]'s alpha for factor 1 (Environmental qualities, infrastructure and security) is 0.889 (12 items), which indicates a high level of internal consistency. Most of the other alphas are medium to high as well: 0.744 (seven items) for factor 2 (Urban health), 0.870 (four items) for factor 3 (Noise stress), 0.806 (three items) for factor 4 (Heat stress), 0.718 (three items) for factor 5 (Cold stress), 0.768 (two items) for factor 6 (Urban services), and 0.600 (two items) for factor 8 (Social network). Only the results for factor 7 (Gender and Consumption) and factor 9 (Age and Social status) indicate a low internal consistency. This is in agreement with the relatively low communalities of the related variables (Table 2). As the factors will not be used for further analyses, the specific problems of factor 7 and 9 will not be addressed; the communalities are still high enough for the variables to be included in the upcoming LR analyses. No substantial increases in alpha for any of the scales were achieved by eliminating items. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Name**} & \multirow{2}{*}{**No. **} & \multirow{2}{*}{**Code**} & \multicolumn{6}{c}{**Component**} & \multicolumn{1}{c}{**Communality**} \\ \cline{5-14}  & & & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & \\ \hline \multirow{8}{*}{**2**} & \multirow{8}{*}{**Urban Health**} & 1. & EQYD & 0.091 & **0.761** & -0.033 & -0.032 & 0.009 & 0.014 & 0.023 & -0.015 & 0.051 & 0.593 \\ \cline{2-14}