Ukuran Sampel dalam SEM PLS

Tulisan berasal dari:
Jorg Henseler, Christian M. Ringle and Rudolf R. Sinkovics (2009),
The Use Of Partial Least Squares Path Modeling In International Marketing, 

New Challenges to International Marketing Advances in International Marketing, Volume 20, 277–319

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The sample size argument has its roots in the considerable obstacles faced when conducting CBSEM with small samples. A substantial number of simulation studies on CBSEM compare alternative discrepancy functions and their estimation bias, accuracy, and robustness with respect to sample size. Boomsma and Hoogland (2001), for example, conclude that there are nonconvergence problems and improper CBSEM solutions in small samples (e.g., 200 or fewer cases). These authors provide evidence that CBSEM – depending on the selected discrepancy function and the model complexity – requires several hundred or even thousands of observations.

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SEM Kovarians menghadapi masalah jika menggunakan ukuran sampel yang kecil. Hasil studi yang dilakukan oleh Boomsma dan Hoogland (2001) terhadap penggunaan sampel kecil dalam SEM Kovarians dengan ukuran "bias estimasi, akurasi, kerobust-an model" menemukan bahwa model SEM Kovarians dengan sampel kecil akan memperoleh permasalahan model tidak konvergen (solusi taksiran parameter model tidak tercapai dan taksiran paramter model tidak tepat). Dengan meningkatnya kompleksitas model maka diperlukan ukuran sampel data yang lebih tinggi (lebih banyak).

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In contrast, the sample size can be considerably smaller in PLS path modeling. For example, ‘‘there can be more variables than observations and there may be a small amount of data that are missing completely at random’’ (Tenenhaus et al., 2005, p. 202). Wold (1989) illustrates the low sample size requirement by analyzing a path model based on a data set consisting of 10 observations and 27 manifest variables. A rule of thumb for robust PLS path modeling estimations suggests that the sample size be equal to the larger of the following (Barclay, Higgins, & Thompson, 1995): (1) ten times the number of indicators of the scale with the largest number of formative indicators, or (2) ten times the largest number of structural paths directed at a particular construct in the inner path model. Chin and Newsted (1999) present a Monte Carlo simulation study on PLS with small samples. They find that the PLS path modeling approach can provide information about the appropriateness of indicators at sample size as low as 20. This study confirms the consistency at large on loading estimates with increased numbers of observations and numbers of manifest variables per measure-ment model.

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Model SEM PLS dapat bekerja dengan sampel yang kecil. Akan tetapi  untuk memperoleh model SEM PLS yang robust maka ukuran sample yang dibutuhkan dalam SEM PLS adalah (1) 10 kali jumlah indikator dalam model pengukuran formatif, (2) 10 kali jumlah model struktural (pengaruh langsung antara variabel laten). Hasil studi yang dilakukan oleh Chin melalui permodelan Monte Carlo menunjukan model SEM PLS membutuhkan minimal 20 pengamatan. Hasil studinya mengkonfirmasi konsistensi pada ukuran sampel besar.

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Salam,

Sofyan Yamin

@2017 Desember, Bogor