The existing latent-standardization method depends on the reliability of the scaled-indicator or the composite scores at the first time point. In this paper, we propose an operable latent-standardization method with two steps. In the first step, a CFA with strong measurement invariance is conducted by fixing the mean and variance of the latent variable at the first time point to 0 and 1 respectively. In the second step, estimated loadings in the first step are employed to establish the second-order LGM. If the standardization is based on the scaled-indicator method, the loading of the scaled-indicator is fixed to that obtained in the first step, and the intercept of the scaled-indicator is fixed to the sample mean of the scaled-indicator at the first time point. If the standardization is based on the effect-coding method, the sum of loadings is constrained to the sum of loadings obtained in the first step, and the sum of intercepts is constrained to the sum of the sample mean of all indicators at the first time point. We also propose a first-order LGM standardization procedure based on the composite scores. First, we standardize the composite scores at the first time point, and make the same linear transformation of the composite scores at the other time points. Then we establish the first-order LGM, which is comparable with the second-order LGM scaled by the latent-standardization method.
The scaling methods of second-order LGMs and their comparable first-order LGMs are systematically summarized. The comparability is illustrated by modeling the empirical data of a Moral Evasion Questionnaire. For the scaled-indicator method, second-order LGMs and their comparable first-order LGMs are rather different in parameter estimates (especially when the reliability of the scale-indicator is low). For the effect-coding method, second-order LGMs and their comparable first-order LGMs are relatively close in parameter estimates. When the latent variable at the first time point is standardized, the mean of the intercept-factor of the first-order LGM is close to 0 and not statistically significant; so is the mean of the intercept-factor of the second-order LGM through the effect-coding method, but those through two scaled-indicator methods are statistically significant and different from each other.
According to our research results, the effect-coding method is recommended to scale and standardize the second-order LGMs, then comparable first-order LGMs are those based on the composite scores and their standardized models. For either the first-order or second-order LGM, the standardized results obtained by modeling composite total scores and composite mean scores are identical.
[V1] | 2023-03-29 10:55:07 | ChinaXiv:202303.02271v1 View This Version | Download |
[V2] | 2023-03-29 10:38:05 | ChinaXiv:202303.02271V2 | Download |
1. 虚拟沟通如何影响上下级权力配置?基于身份自构和互构的视角 | 2024-06-09 |
2. 数媒时代焦虑抑郁与社会比较的关系:一项系统综述 | 2024-06-08 |
3. 客体类别调节跨通道冲突感觉主导效应 | 2024-06-06 |
4. 融合中国诗词的线上自助正念干预的可行性及对参与者依从性的影响 | 2024-06-06 |
5. 为何人际价值观冲突难以达成共识?理论解释及调解策略 | 2024-06-06 |
6. 如何提高人类幸福感:个体、人际和社会的多层次机制 | 2024-06-06 |
7. 狄考文与晚清时期心理学的传播 ——从心灵学课程最早开设的学校谈起 | 2024-06-06 |
8. 数字在场与具身离场:身体—技术关系模式下MMORPG中的浪漫关系研究 | 2024-06-05 |
9. 路线难度和交互方式对行人寻路绩效的影响 | 2024-06-05 |
10. 将功补过!基于身份维护视角的家庭-工作冲突作用机制 | 2024-06-05 |