Longitudinal item factor analysis and growth modeling

--- title: Longitudinal item factor analysis and growth modeling tags: AdPsy2021, Talk description: View the slide with "Slide Mode". slideOptions: theme: white --- ## Longitudinal item factor analysis and growth modeling **蔡介文** 2021/3/15 ideas/topics --- ![](https://i.imgur.com/7JvvV6a.png) --- ### Studies - Study 1：Treat Likert-type scale as continuous data vs. categorical data. :::success **目的：實作類別資料的因素分析，並希望能接到 SEM 上面。** 目前以 Study 1 為主，用真實資料（e.g. 台灣青少年成長歷程研究/自尊）試試看實現 item factor analysis。用 2PL graded response model、或 1PL partial credit model 等等。比較看看跟總分的形狀有什麼不同？並看看能不能結合 SEM。 ::: :::danger **可能需要解決的問題** - 真實資料：台灣青少年成長歷程研究/自尊，這很多人做過了。但是用 item factor analysis 處理的好像是沒有。 - 模擬資料： - 估計：MLE, EM, MCMC, etc. - measurement invariance over time 的問題。 ::: - Study 2：LV 為 time point，LV 為 change score。 - Study 3：真實資料、模擬資料。 --- ### 長期資料的測量在研究成長模型與 IRT 相關文章時，發現一個實務上的問題：成長模型需要比較不同時間點的潛在分數，但是這個分數怎麼得出來？ Blanchin、Hardouin、Neel、Kubis、Blanchard、Mirallié 與 Sébille（2010）比較了 CTT、Rasch、PV（可能值）、longitudinal mixed Rasch model（LRM）等四種方法，結果以 LRM 最佳，並不建議用 PV。Gorter、Fox、Riet、Heymans 與 Twisk（2020）的文章中，引入 MCMC 方法與可能值的方法處理 CTT 與 IRT 分數後進行比較。但是根據 `Bacci（2012）`，先用 IRT 模型算出各波次的數值，再用迴歸模型分析資料的「二階段法」，雖然簡便但卻有許多問題。他比較了 LLTM/LLRM 方法與 MIRT 法。Wang 與 Nydick（2020）則詳細比較了 L-UIRT、L-MIRT、L-HO-IRT（longitudinal higher order IRT）等更多種類的 IRT 方法。 Mair（2017）在「Modern Psychometrics with R」書中整理了 longitudinal IRT 的處理方式： :::success 1. linear logistic models (LLTM/LLRM) ，`（Fischer, 1995）` 2. two-tier item factor model，`（Cai, 2010）` 3. IRT 潛在成長模型（latent growth IRT models）。如果是根據 `McArdle 與 Grimm（2010）`等學者的推廣，則還包括潛在改變分數模型。（還沒看懂） ::: 當然，還包括成長模型中的次序性成長模型。從上述簡單的整理可知：成長模型的基礎在於要有各波次的分數（無論是觀察的或是潛在的），測量分數直接影響到後面成長模型的估計與解釋。但各波次的分數如何得到（尤其是使用量表測量的分數），甚至需不需要得到（如 Bacci, 2012）至今仍在討論。所以我在想這或許也是一個值得探討的問題？（而且跟 IRT 、成長模型息息相關。） --- ### Item factor analysis - Grimm, K. J., Ram, N., & Estabrook, R. (2017). *Growth modeling: Structural equation and multilevel modeling approaches*. NY: Guilford Press. - Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: current approaches and future directions. *Psychological methods, 12*(1), 58–79. https://doi.org/10.1037/1082-989X.12.1.58 - Jöreskog, K. G., & Moustaki, I. (2001). Factor Analysis of Ordinal Variables: A Comparison of Three Approaches. *Multivariate behavioral research, 36*(3), 347–387. https://doi.org/10.1207/S15327906347-387 - Liu, Y., Millsap, R. E., West, S. G., Tein, J. Y., Tanaka, R., & Grimm, K. J. (2017). Testing measurement invariance in longitudinal data with ordered-categorical measures. *Psychological methods, 22*(3), 486–506. ### Latent change score - [Wang, C., & Nydick, S. W. (2020). On longitudinal item response theory models: A didactic. Journal of Educational and Behavioral Statistics, 45(3), 339-368. doi:10.3102/1076998619882026.](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/EYimAVvYAG1HgDA_e6OyPeoBs4h7Ock35k-ZOOSIJwn0UQ?e=7CwvBT) - [McArdle, J. J. (2009). Latent Variable Modeling of Differences and Changes with Longitudinal Data. Annual Review of Psychology, 60(1), 577--605. doi:10.1146/annurev.psych.60.110707.163612](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/EasSMUJLZtVAiUPFaFUMn0MBOzCNJhLr6uWVy6cf-kbXkA?e=FVpnkU) - [Erbeli, F., Shi, Q., Campbell, A. R., Hart, S. A., & Woltering, S. (2020). Developmental Dynamics Between Reading and Math in Elementary School. Developmental Science, e13004.](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/EVHAHbrJKuxHnoys3GojETsBXQWzSUr1yO2drMbHmj3aFA?e=zRyfV8) - [Millsap, R. E. (2010). Testing measurement invariance using item response theory in longitudinal data: An introduction. Child Development Perspectives, 4(1), 5-9.](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/EVjHIs2MJzZKqTkymYnDk9QBAVumWtCAw4UfDnsumIVRsg?e=Jztn3M) ==（測量不變性）== - [**Ghisletta, P., & McArdle, J. J. (2012). Latent curve models and latent change score models estimated in R. Structural equation modeling: a multidisciplinary journal, 19(4), 651-682.**](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/EQL97rpQfihKhvkj7K05nD4Bw2-02z73MgRQ4oPgCaJfmw?e=wnUAZh) - [Grimm, K. J., An, Y., McArdle, J. J., Zonderman, A. B., & Resnick, S. M. (2012). Recent changes leading to subsequent changes: Extensions of multivariate latent difference score models. Structural equation modeling: a multidisciplinary journal, 19(2), 268-292.](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/EWhdkFAbbllCguzwCRTdyJABvMQYuuhi4GorS02GuJzgZg?e=ffvUbW) ### MIRT - [Immekus, J. C., Snyder, K., & Ralston, P. A. (2019). Multidimensional Item Response Theory for Factor Structure Assessment in Educational Psychology Research. In Frontiers in Education (Vol. 4, p. 45). Frontiers.](https://www.frontiersin.org/articles/10.3389/feduc.2019.00045/full) - [Bacci, S. (2012). Longitudinal data: different approaches in the context of item-response theory models. Journal of Applied Statistics, 39(9), 2047-2065. DOI: 10.1080/02664763.2012.700451](https://mail3nccu-my.sharepoint.com/:b:/g/personal/109152512_mail3_nccu_tw/ESYFzPgm0HBNgtNSpippkNABWsw4NTrhSjysGgrptzrVvg?e=1CkBRS) - McArdle, J. J., & Grimm, K. J. (2010). Five steps in latent curve and latent change score modeling with longitudinal data. In Longitudinal research with latent variables (pp. 245-273). Springer, Berlin, Heidelberg. - **Grimm, K. J., Ram, N., & Estabrook, R. (2016). Growth modeling: Structural equation and multilevel modeling approaches. Guilford Publications.** - Fischer, G. H. (1995). Linear logistic models for change. In Rasch models (pp. 157-180). Springer, New York, NY. - Measuring Change Using Rasch Models（Gerhard H. Fischer），收錄於 Handbook of item response theory: volume three, applications: edited by Wim J. van der Linden, Boca Raton, FL, CRC Press. - Anselmi, P., Vidotto, G., Bettinardi, O., & Bertolotti, G. (2015). Measurement of change in health status with Rasch models. Health and quality of life outcomes, 13(1), 1-7.