Sains Malaysiana 44(10)(2015): 1531–1540

Application of Functional Data Analysis for the Treatment of Missing Air Quality Data

(Aplikasi Analisis Data Fungsian untuk Merawat Data Kualiti Udara yang Lenyap)

NORSHAHIDA SHAADAN¹*, SAYANG MOHD DENI¹ & ABDUL AZIZ JEMAIN²

¹Center for Statistical and Decision Science Studies, Faculty of Computer & Mathematical Sciences

Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor Darul Ehsan, Malaysia

²DELTA, School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 26 Mac 2014/Diterima: 15 Jun 2015

ABSTRACT

In most research including environmental research, missing recorded data often exists and has become a common problem for data quality. In this study, several imputation methods that have been designed based on the techniques for functional data analysis are introduced and the capability of the methods for estimating missing values is investigated. Single imputation methods and iterative imputation methods are conducted by means of curve estimation using regression and roughness penalty smoothing approaches. The performance of the methods is compared using a reference data set, the real PM₁₀ data from an air quality monitoring station namely the Petaling Jaya station located at the western part of Peninsular Malaysia. A hundred of the missing data sets that have been generated from a reference data set with six different patterns of missing values are used to investigate the performance of the considered methods. The patterns are simulated according to three percentages (5, 10 and 15) of missing values with respect to two different sizes (3 and 7) of maximum gap lengths (consecutive missing points). By means of the mean absolute error, the index of agreement and the coefficient of determination as the performance indicators, the results have showed that the iterative imputation method using the roughness penalty approach is more flexible and superior to other methods.

Keywords: Air quality; functional data; imputation; missing value; PM₁₀

ABSTRAK

Dalam kebanyakan penyelidikan termasuklah penyelidikan alam sekitar, data lenyap sering wujud dalam rekod dan telah menjadi masalah lazim terhadap kualiti data. Dalam kajian ini, beberapa kaedah imputasi yang berasaskan teknik analisis data fungsian telah dicadangkan dan kebolehan kaedah tersebut dikaji. Kaedah imputasi tunggal dan kaedah imputasi ulangan telah dijalankan dengan pendekatan penganggaran lengkuk menggunakan teknik pelicinan regresi dan teknik denda kekasaran. Prestasi kaedah-kaedah imputasi dibandingkan menggunakan data set rujukan cerapan sebenar pencemar PM₁₀ yang telah direkodkan di stesen pemantau kualiti udara Petaling Jaya yang terletak di bahagian barat Semenanjung Malaysia. Untuk mengkaji prestasi kaedah imputasi yang dicadangkan, sebanyak seratus data set dijana untuk setiap enam paten data lenyap yang berbeza menggunakan data rujukan. Paten kelenyapan data disimulasi mengikut tiga jumlah nilai peratusan kelenyapan (5, 10 dan 15) dengan dua saiz maksimum panjang turutan kelenyapan (3 dan 7) (titik lenyap berturut). Dengan kaedah min ralat mutlak, indeks persetujuan dan nilai pekali penentu sebagai penunjuk prestasi, keputusan analisis kajian mendapati bahawa kaedah imputasi ulangan yang menggunakan pendekatan denda kekasaran adalah lebih fleksibel dan lebih baik daripada kaedah yang lain.

Kata kunci: Data fungsian; imputasi; kualiti udara; nilai lenyap; PM₁₀

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*Pengarang untuk surat-menyurat; email: shahida@tmsk.uitm.edu.my