Spatial Structural Equation Modeling Dengan Pendekatan Generalized Method Of Moments Studi Kasus: Pemodelan Kualitas Pendidikan Tingkat SMA Kabupaten Sumenep

Anekawati, Anik (2020) Spatial Structural Equation Modeling Dengan Pendekatan Generalized Method Of Moments Studi Kasus: Pemodelan Kualitas Pendidikan Tingkat SMA Kabupaten Sumenep. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Variabel laten memiliki hubungan kausalitas sekaligus mempunyai pengaruh secara spasial terjadi untuk beberapa kasus penelitian. Permasalahan tersebut diatasi dengan memasukkan unsur spasial ke dalam model Structural Equation Modeling (SEM). Pada penelitian ini, pelibatan bobot spasial ditempatkan pada model struktural dan menggunakan metode pembobotan queen contiguity. Skor faktor pada model SEM spasial (mengasumsikan distribusi error model sama dengan model spasial tradisional) diestimasi menggunakan Partial Least Square (PLS). Parameter Spatial Autoregressive Model pada SEM (SAR-SEM) diestimasi menggunakan metode Two Stage Least Square (2SLS), sedangkan Spatial Error Model pada SEM (SERM-SEM) menggunakan metode Generalized Method of Moments (GMM). Skor faktor dari SAR-SEM (tidak mengasumsikan distribusi error model sama dengan distribusi error model spasial tradisional) diestimasi menggunakan metode Weighted Least Square (WLS) dan parameter model diestimasi menggunakan 2SLS.
Hasil penaksir parameter, bentuk statitistik uji LM, dan bentuk statistik uji parameter untuk model SEM spasial (dengan asumsi) adalah sebagai berikut: penaksir parameter model SAR-SEM dan SERM-SEM adalah δ=(Z’PHZ)-1Z’PHl dan (ρ,ρ2,σε2)= (G’G)-1G’g. Bentuk statistik uji dependensi spasial model SAR-SEM dan SERM-SEM adalah LMλ=((Wl)’ẽ/σε2)2/J dan LMρ=(ẽ’Wẽ /σε2)2/T. Uji MLRT untuk model SAR-SEM dan SERM-SEM yaitu (Λ-2/n-1)(n-p)/((n-1)p) dimana Λ-2/n=│∑(li-Qβ0)’(li-Qβ0)/∑(li-Q(β0+Kβ))’(li-Q(β0+Kβ))│. Pada tingkat signifikansi α, H0 ditolak jika (Λ-2/n-1)(n-p)/((n-1)p)>F(p,n-p(α)). Model SAR-SEM (tanpa asumsi) adalah l=Kβ+λWl+ε dengan error berdistribusi ε ̴̴ N((I-λW)eƞt- Kβ,Ɵ). Skor faktor eksogen dan endogen adalah ∑ξt=(Λ’XƟδ-1ΛX)-1(Λ’XƟδ-1)∑xt dan ∑ηt=(Λ’yƟε-1Λy)-1(Λ’yƟε-1) ∑yt, hasil estimasi parameter adalah δ=(Z’PHZ)-1Z’PHl dan dan bentuk uji LM adalah LMλ=-(p(W Kβ)’ẽ)2/pD serta bentuk dan distribusi statistik uji untuk pengujian hipotesis model menggunakan MLRT adalah (Λ-2/n-1)(n-p)/((n-1)p) dimana Λ-2/n(li-eƞ)’(li-eƞ)/∑(li- (eƞ-Kβ))’(li-(eƞ-Kβ))│. Pada tingkat signifikansi α, H0 ditolak jika (Λ-2/n-1)(n-p)/((n-1)p)>F(p,n-p(α)).
Hasil aplikasi model SEM spasial baik yang menggunakan asumsi atau tidak, keduanya mengarah ke model SAR-SEM. Kedua model menunjukkan hanya variabel Sarana Prasarana yang mempengaruhi variabel Kualitas Pendidikan, sedangkan variabel Sosial Ekonomi tidak berpengaruh.
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In some cases, latent variables could have not only a causal relationship but also a spatial effect. To investigate the spatial effect, a spatial element could be included in the Structural Equation Modeling (SEM). In this study, a spatial weight was given on the structural model using the spatial weight method of the queen contiguity. Factor scores on the spatial SEM model were estimated using the Partial Least Square (PLS) method, assuming that the model error distribution and error distribution of the traditional spatial model was the same. The parameters of the Spatial Autoregressive Model in SEM (SAR-SEM) were estimated using the Two-Stage Least Square (2SLS) method, while the Spatial Error Model in SEM (SERM-SEM) used the Generalized Method of Moments (GMM) method. Without the assumption that the error distribution of the SEM model and the traditional spatial model was the same, the factor scores of the SAR-SEM were estimated using the Weighted Least Square (WLS) method, and the parameters were estimated using 2SLS.
The results of parameter estimator, LM test statistical form, and parameter test statistical form for spatial SEM model (with assumptions) were as follows: the parameter estimator of SAR-SEM and SERM-SEM model were δ=(Z’PHZ)-1Z’PHl and (ρ,ρ2,σε2)= (G’G)-1G’g. The LM test statistical form of SAR-SEM and SERM-SEM model respectively were LMλ=((Wl)’ẽ/σε2)2/J and LMρ=(ẽ’Wẽ /σε2)2/T. The MLRT test of SAR-SEM and SERM-SEM model was (Λ-2/n-1)(n-p)/((n-1)p) with Λ-2/n=│∑(li-Qβ0)’(li-Qβ0)/∑(li-Q(β0+Kβ))’(li-Q(β0+Kβ))│. At the significance level of α decided that H0 was rejected if (Λ-2/n-1)(n-p)/((n-1)p)>F(p,n-p(α)).
The SAR-SEM (without the assumption) was l=Kβ+λWl+ε and distribution error was ε ̴̴ N((I-λW)eƞt- Kβ,Ɵ). The factor score of exogenous and endogenous respectively were ∑ξt=(Λ’XƟδ-1ΛX)-1(Λ’XƟδ-1)∑xt and ∑ηt=(Λ’yƟε-1Λy)-1(Λ’yƟε-1)∑yt, the result of parameter estimator was δ=(Z’PHZ)-1Z’PHl, and LM test was LMλ=-(p(W Kβ)’ẽ)2/pD as well as MLRT test was (Λ-2/n-1)(n-p)/((n-1)p) with Λ-2/n(li-eƞ)’(li-eƞ)/∑(li-(eƞ-Kβ))’(li-(eƞ-Kβ))│. At the significance level of α decided that H0 was rejected if (Λ-2/n-1)(n-p)/((n-1)p)>F(p,n-p(α)). The results of the applied studies for both spatial SEM models with and without the error distribution assumption led to the SAR-SEM. Both models showed that the Infrastructure variable influenced the Education Quality variable, while the Socio-economic variable did not affect it.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	SEM Spasial, SAR-SEM, SERM-SEM, PLS, WLS, GMM Spatial SEM, SAR-SEM, SERM-SEM, PLS, WLS, GMM
Subjects:	Q Science > QA Mathematics > QA275 Theory of errors. Least squares. Including statistical inference. Error analysis (Mathematics) Q Science > QA Mathematics > QA278.5 Principal components analysis. Factor analysis. Correspondence analysis (Statistics) Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Anik Anekawati
Date Deposited:	18 Dec 2020 03:57
Last Modified:	18 Dec 2020 03:57
URI:	http://repository.its.ac.id/id/eprint/82320

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