Factor analysis is a commonly used method of modelling correlated multivariate exposure data. Typically, the measurement model is assumed to have constant factor loadings. However, from our preliminary analyses of the Environmental Protection Agency's (EPA's) PM2.5 fine speciation data, we have observed that the factor loadings for four constituents change considerably in stratified analyses. Since invariance of factor loadings is a prerequisite for valid comparison of the underlying latent variables, we propose a factor model that includes non-constant factor loadings that change over time and space using P-spline penalized with the generalized cross-validation (GCV) criterion. The model is implemented using the Expectation-Maximization (EM) algorithm and we select the multiple spline smoothing parameters by minimizing the GCV criterion with Newton's method during each iteration of the EM algorithm. The algorithm is applied to a one-factor model that includes four constituents. Through bootstrap confidence bands, we find that the factor loading for total nitrate changes across seasons and geographic regions.

中文翻译：

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使用具有非恒定因子载荷的潜变量模型来检查与二次无机气溶胶相关的 PM2.5 成分。


因子分析是对相关多变量暴露数据进行建模的常用方法。通常，假设测量模型具有恒定的因子载荷。然而，根据我们对环境保护局 (EPA) PM2.5 精细形态数据的初步分析，我们观察到四种成分的因子载荷在分层分析中发生了很大变化。由于因子载荷的不变性是有效比较潜在变量的先决条件，因此我们提出了一个因子模型，其中包括使用受广义交叉验证（GCV）标准惩罚的 P 样条随时间和空间变化的非常量因子载荷。该模型是使用期望最大化（EM）算法实现的，我们在 EM 算法的每次迭代期间通过使用牛顿法最小化 GCV 准则来选择多个样条平滑参数。该算法应用于包含四个成分的单因素模型。通过引导置信带，我们发现总硝酸盐的因子载荷随着季节和地理区域的变化而变化。