[ Technical Information ]
Asian Journal of Atmospheric Environment - Vol. 14, No. 1, pp.62-72
ISSN: 1976-6912 (Print) 2287-1160 (Online)
Print publication date 31 Mar 2020
Received 28 Nov 2019 Revised 28 Jan 2020 Accepted 07 Feb 2020

# Missing Value Imputation for PM10 Concentration in Sabah using Nearest Neighbour Method (NNM) and Expectation-Maximization (EM) Algorithm

Muhammad Izzuddin Rumaling1) ; Fuei Pien Chee1), * ; Jedol Dayou1) ; Jackson Hian Wui Chang2), 3) ; Steven Soon Kai Kong3) ; Justin Sentian4)
1)Faculty of Science and Natural Resources (FSNR), Universiti Malaysia Sabah, Kota Kinabalu, Sabah
2)Preparatory Centre for Science and Technology, Universiti Malaysia Sabah, Kota Kinabalu, Sabah
3)Cloud and Aerosol Laboratory, Department of Atmospheric Science, National Central University, Taoyuan
4)Climate Change Research Group (CCRG), FSNR, Universiti Malaysia Sabah, Kota Kinabalu, Sabah

Correspondence to: * Tel: +60-88-320-000 E-mail: fpchee06@gmail.com

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

## Abstract

Missing data in large data analysis has affected further analysis conducted on dataset. To fill in missing data, Nearest Neighbour Method (NNM) and Expectation Maximization (EM) algorithm are the two most widely used methods. Thus, this research aims to compare both methods by imputing missing data of air quality in five monitoring stations (CA0030, CA0039, CA0042, CA0049, CA0050) in Sabah, Malaysia. PM10 (particulate matter with aerodynamic size below 10 microns) dataset in the range from 2003-2007 (Part A) and 2008-2012 (Part B) are used in this research. To make performance evaluation possible, missing data is introduced in the datasets at 5 different levels (5%, 10%, 15%, 25% and 40%). The missing data is imputed by using both NNM and EM algorithm. The performance of both data imputation methods is evaluated using performance indicators (RMSE, MAE, IOA, COD) and regression analysis. Based on performance indicators and regression analysis, NNM performs better compared to EM in imputing data for stations CA0039, CA0042 and CA0049. This may be due to air quality data missing at random (MAR). However, this is not the case for CA0050 and part B of CA0030. This may be due to fluctuation that could not be detected by NNM. Accuracy evaluation using Mean Absolute Percentage Error (MAPE) shows that NNM is more accurate imputation method for most of the cases.

## Keywords:

Particulate matter, Missing data, Nearest neighbour method, Expectation maximization algorithm, Performance indicators

## 1. INTRODUCTION

Air quality monitoring in Malaysia is continuously conducted by Department of Environment (DOE) and is done in stations around Malaysia (Dominick et al., 2012). These stations collect PM10 concentration data at one-hour interval. However, due to maintenance, calibration of monitoring instruments and power outage, data collected by monitoring stations may suffer missingness. Missing data mechanism can be categorized into three different types: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) (Nakai and Ke, 2011). Missingness is categorized as MNAR when it depends on the missing value itself. MNAR is known to be non-ignorable and missing data due to MNAR is not possible to be recovered (Graham, 2009). On the other hand, missingness due to MAR depends on the observed data. MAR is ignorable and missing data can be recovered because its missingness does not depend on missing data itself. MCAR is a special case of MAR, where missingness is independent of both missing data and observed data (Dong and Peng, 2013). A set of data containing missing data due to MCAR can be considered as complete dataset because the missingness does not introduce bias (Dong and Peng, 2013). Little’s MCAR test can be used to determine whether the missingness is due to MCAR (Li, 2013). If the missingness is not MCAR instead, this test cannot be used to determine whether the missingness is due to MAR or MNAR (Dong and Peng, 2013). In terms of air quality data in Malaysia, missingness can be considered as MAR because the missingness is mainly caused by maintenance, calibration of monitoring instruments and power outage. It does not depend on whether the value of data is lower or higher than certain value. Missingness can affect further analysis that requires complete dataset such as Fourier analysis and principal component analysis.

Particulate matter (PM) is mixture of substances in the form of small particles suspended in the air. PM is one of the critical components of air pollution (Li et al., 2017b). Due to its small size, PM can enter respiratory system, thus becoming one of major concerns in public health (Chang et al., 2018). Because of this, scientific attraction has been attracted towards PM (Shahraiyni and Sodoudi, 2016). PM mainly comes from motor vehicles, dust from construction sites and landfills. It also comes from biomass burning and brought by haze, a typical challenge in Southeast Asia since 1980s (Shaadan et al., 2015). PM10 (particulate matter with aerodynamic diameter less than 10 microns) is one of major concern because it possesses hazardous properties towards human health compared to other pollutants such as carbon monoxide and nitrogen dioxide (Kim et al., 2015; Ny and Lee, 2010). This is because it can enter respiratory system while defending natural defences of human body (Chang et al., 2018). PM10 can increase risk of asthma, aggravate bronchitis, respiratory syncytial virus (RSV) bronchiolitis and other lung diseases (Carugno et al., 2018; Lelieveld et al., 2015). This is especially true for children aged between 5-15 years (Cadelis et al., 2014). Other than respiratory problems, cardiovascular disease and cancer can be developed due to PM10 in the air (Li et al., 2017a).

Many agencies around the world such as European Union (EU) and World Health Organization (WHO) implemented guidelines and set limit on air pollution concentration levels (Abd. Rani et al., 2018). In Malaysia, the guidelines are implemented by DOE. According to New Malaysia Ambient Air Quality Standard, PM10 concentration has its standard set to 50 μg/m3 (1-year averaging time) on 2015 before it is gradually lowered to 40 μg/m3 by 2020 (Department of Environment, n. d.). The implementation of this standard is important in order to ensure that air quality can be maintained at safe level. Therefore, there is a need to continuously monitor ambient air quality around Malaysia.

This research focuses on evaluating performance of data imputation on air quality data from five monitoring stations around Sabah. To make performance evaluation possible, missingness is introduced to compare observed data with imputed data. Two methods of data imputation are studied in this research, namely Nearest Neighbour Method (NNM) and Expectation-Maximization (EM) algorithm. Many previous studies have employed nearest neighbour method and expectation-maximization algorithm to obtain complete dataset. However, not many of these studies emphasize on the efficiency of these two methods in data imputation. By comparing between both NNM and EM algorithm, further analysis that requires complete dataset can be made more accurate.

## 2. DATA AND METHODS

### 2. 1 Study Area and Data

Five monitoring stations (CA0030, CA0039, CA0042, CA0049, CA0050) in Sabah are listed in Table 1. Respective cities of each monitoring station are located as shown in Fig. 1. Except for CA0049, other monitoring stations are located at low altitudes and are close to the sea. Furthermore, Labuan (CA0050) is situated on a small island located at western of Sabah. As shown in Fig. 2, PM10 concentration in Sabah differs between seasons and location (Kanniah et al., 2016). Western coast of Sabah generally has higher PM10 concentration compared to other parts of Sabah all-year round. Also, PM10 concentration in Sabah is generally lower during intermonsoon October.

Location of monitoring stations in Sabah.

Location of PM10 monitoring stations at urban and suburban areas (Kota Kinabalu, Tawau, Sandakan, Keningau, Labuan) in Sabah.

Spatial distribution of estimated PM10 concentration in Sabah from 2007-2011 for (a) dry season (June-September), (b) wet season (November-March), (c) intermonsoon (April-May), and (d) intermonsoon (October) based on MODIS-AOD500 and meteorological variables (Kanniah et al., 2016).

These monitoring stations, operated by DOE, continuously measures PM10 concentration data at 1-hour interval. PM10 concentration is measured using tapered element oscillating microbalance (TEOM), with temporal resolution of 1 h. As wind direction is angular quantity, wind speed and direction must be converted into x-component (east-west) and y-component (north-south) wind speed using equations (1) and (2). This prevents difficulty in analysis due to nature of angular quantity (Muhammad Izzuddin et al., 2019; Kovač-Andrić et al., 2009).

 ${W}_{x}={W}_{s}\mathrm{sin}{W}_{d}$ (1)
 ${W}_{y}={W}_{s}\mathrm{cos}{W}_{d}$ (2)

For the purpose of this research, 10-year hourly data from 2003 to 2012 are divided into two parts. The first part (Part A) ranges from 2003 to 2007, while the second part (Part B) ranges from 2008 to 2012. Due to climate change, trends of PM10 concentration data may differ from both parts. Thus, both parts may have difference in these data.

### 2. 2 Introduce Missingness to Data

In order to ensure that imputed data can be validated, a fraction of observed data must be replaced by missingness. Depending on complexity, missingness is introduced into data by percentage as conducted in previous research by Noor et al. (2014) as shown in Table 2. A sequence of zeros and ones (0 - do not replace observed data, 1 - replace observed data with missingness) is randomly generated using MATLAB 2018b and is used as a reference to introduce missingness to observed data. The actual percentage after introducing missingness may deviate by up to 2% due to existing missingness in the data.

Percentage of missingness as conducted by Noor et al. (2014).

### 2. 3 Data Imputation

A lot of data imputation method has been proposed for temporal dataset (Bai et al., 2019). Due to simplicity, two of the most popular methods used in data imputation are NNM and EM. NNM is common in replacing missing air quality data (Li and Liu, 2014; Dominick et al., 2012). For a stream of missing data bounded by observed data (x1, y1) in lower bound and (x2, y2) in upper bound, missing data is replaced with a value calculated using equations (3) and (4) (Abd Rani et al., 2018; Zakaria and Noor, 2018; Siti Zawiyah et al., 2010; Junninen et al., 2004). NNM is performed by executing a code developed using MATLAB 2018b.

 (3)
 $\overline{x}=\frac{{x}_{2}-{x}_{1}}{2}$ (4)

EM algorithm employs a set of iterative equations to estimate mean vector and covariance matrix of multivariate distribution from exponential family (Junger and de Leon, 2015). This method maximizes log likelihood to find parameters when there are missing values (Nakai and Ke, 2011). The simplicity and smooth operation of EM algorithm makes it unique among present multiple imputation methods. In addition, its faster operation compared to the alternatives makes EM algorithm one of the most popular imputation methods (Abd Rani et al., 2018).

Given a set of data consisting of observed data Dobs and missing data Dmis, EM algorithm starts by defining parameter θ as a random value. Then, E-step (expectation step) calculates the likelihood of each values of Dmis for every missingness. M-step (maximization step) uses computed values of Dmis to find better estimation of θ. Given the likelihood function L and expected value of log likelihood function Q (θ|θ(t)), both E-step and M-step iterate until the value converges (Abd Rani et al., 2018). Both E-step and M-step are executed using equations (5) and (6).

 (5)
 ${\theta }^{\left(t+1\right)}=\mathrm{arg}\mathrm{max}Q\left(\theta |{\theta }^{\left(t\right)}\right)$ (6)

### 2. 4 Performance Evaluation

The performance of data imputation is evaluated by using performance indicators. The performance indicators that have been used are root mean square error (RMSE), mean absolute error (MAE), index of agreement (IOA), and coefficient of determination (COD). The performance indicators are calculated by using equations (7) to (10) (Abd. Rani et al., 2018; Nuryazmin et al., 2015; Ul-Saufie et al., 2013; Junninen et al., 2004):

 $RMSE=\sqrt{\frac{1}{n-1}{\sum }_{i=1}^{n}{\left({P}_{i}-{O}_{i}\right)}^{2}}$ (7)
 $MAE=\frac{1}{n}\sum _{i=1}^{n}\left|{P}_{i}-{O}_{i}\right|$ (8)
 $IOA=1-\frac{{\sum }_{i=1}^{n}{\left({P}_{i}-{O}_{i}\right)}^{2}}{{\sum }_{i=1}^{n}{\left(\left|{P}_{i}-\overline{O}\right|+\left|{O}_{i}-\overline{O}\right|\right)}^{2}}$ (9)
 $COD={R}^{2}={\left(\frac{{\sum }_{i=1}^{n}\left({P}_{i}-\overline{P}\right)\left({O}_{i}-\overline{O}\right)}{n\cdot {s}_{p}\cdot {s}_{o}}\right)}^{2}$ (10)

where n is total number of data, Pi is predicted value of ith data, Oi is observed value of ith data, $\overline{P}$ is mean predicted value, $\overline{O}$ is mean observed value, sp is standard deviation of predicted values, and so is standard deviation of observed values.

### 2. 5 Mean Absolute Percentage Error (MAPE)

Mean absolute percentage error (MAPE) is a measure that evaluates accuracy of a prediction model (Khair et al., 2017). MAPE indicates error in predicting the value of missing data when comparing to real value. MAPE is calculated using equation (11) as follows (Khair et al., 2017).

 $MAPE=\frac{1}{n}\sum _{i=1}^{n}\frac{\left|{O}_{i}-{P}_{i}\right|}{{O}_{i}}×100%$ (11)

## 3. RESULT AND DISCUSSION

### 3. 1 Performance Indicators

PM10 concentration datasets for five monitoring stations in Sabah are analysed. RMSE, MAE, IOA, and COD are calculated for every percentage of missingness and station for both part A and B. Tables 3 and 4 reveals performance indicators for NNM and EM at 5 missingness levels and 5 different stations for part A and part B respectively. The desirable attributes between these methods are highlighted in bold. In terms of missingness level, there is no definite relationship between performance of data imputation and missingness level. This is because both NNM and EM impute missing data based on available data. As long as available data is sufficient, missing data can still be effectively imputed.

Performance indicators for every station and missingness percentage for part A.

Performance indicators for every station and missingness percentage for part B.

Most of the data show that nearest neighbour method is better imputation method. This may be due to the nature of missingness in relation to ability of EM algorithm to impute data. EM algorithm works best for missing data caused by MCAR (Nakai and Ke, 2011; Graham, 2009). However, air quality data collected in monitoring stations are not caused by MCAR as the cause of missingness is known. This may attribute to lower performance of EM algorithm compared to NNM.

However, this is not the case for CA0050, where most of the performance indicators for that station show that EM algorithm is a better imputation method. This may be due to the fact that Labuan is surrounded by sea. One study has shown that air humidity is affected by bodies of water due to high heat capacity and strong evaporation (Zhu and Zeng, 2018). Furthermore, cold-wet air that surrounds a water body enhances air flow away from bodies of water by changing the local air circulation (Zhu and Zeng, 2018). The local air circulation highly affects humidity in Labuan. Another study suggests that different levels of humidity affects PM10 concentration differently (Lou et al., 2017). PM10 concentration increases with humidity up to 60%. Beyond that point, gravity deposition occurs and PM10 concentration begins to drop (Lou et al., 2017). PM10 concentration as monitored by CA0050 may fluctuate due to continually changing of humidity level, traffic congestion and active industrial activity. This fluctuation is not accounted by NNM, leading to indication that EM algorithm is better imputation method for data collected by CA0050.

As for PM10 concentration read by CA0030, several performance indicators show that EM algorithm is better imputation method especially for part B of the data. This may be due to fluctuation of PM10 concentration in Kota Kinabalu especially between year 2008 and 2012. One study shows that PM10 concentration from 16th to 18th January 2012 spiked at 7.00 a.m. and fluctuates at the other time (Chang et al., 2018). When this portion of data is missing, NNM may not be able to restore the missingness as well as EM algorithm.

### 3. 2 Regression Analysis on Imputed Data

The performance of data imputation is further evaluated by calculating correlation of coefficient R on predicted data against observed data. The most ideal case of imputed data occurs when predicted data equals observed data (R=1). Tables 5 and 6 reveals coefficient of correlation of data in part A and B respectively, for all five missingness percentages and five stations.

Coefficient of correlation for dataset in Part A.

Coefficient of correlation for dataset in Part B.

Similar to performance indicators, coefficient of correlation shows that NNM is better imputation method for monitoring stations in Tawau, Sandakan and Keningau. As for CA0030, NNM is better imputation method for Part A, but not in Part B. Dataset recorded by CA0050 strongly suggests that EM algorithm is better imputation method.

Fig. 3 reveals scatter plot of data imputation for both CA0042 and CA0050. CA0042 and CA0050 are selected to be presented in the Fig. 3 because CA0042 is located at high altitude while CA0050 is located in a small island. The predicted-observed regression is shown for both stations due to different geographical condition in contrast to the other three stations. Coefficient of correlation for CA0042 shows relatively large difference between two methods compared to other stations. As shown in Fig. 3, all scatter plots for CA0042 shows that line representing NNM is closer to dashed line compared to line that represents EM algorithm. This shows that NNM has greater tendency to predict missing data closer to observed data compared to EM algorithm. This might be caused by missingness mechanism, in which data is Missing at Random. EM algorithm may not be able to impute MAR data as well as MCAR data (Nakai and Ke, 2011; Graham, 2009).

Scatter plot for imputation of data from CA0042 and CA0050 for part A and B at various missingness percentage. Blue indicates NNM, red indicates EM, while dashed line represents the point where predicted data equals observed data.

Meanwhile, CA0050 shows that EM algorithm gives better coefficient of correlation in contrast to other stations. Despite that, Fig. 3 reveals that NNM has either greater tendency (Part A) or approximately similar to EM algorithm (Part B) to predict missing data. This is because the lines representing NNM and EM are plotted at best fit. However, the scatter plot shows that imputed data by NNM for CA0050 are more dispersed away from line of best fit compared to that of CA0042, which might contribute to lower R value of NNM compared to EM algorithm. Although best fit line for NNM is closer to dashed line, the dispersion of scatter plot shows that EM algorithm is better imputation method compared to NNM.

### 3. 3 Mean Absolute Percentage Error (MAPE)

Performance of data imputation is further evaluated using MAPE. Data imputation is most accurate when MAPE approaches zero. Table 7 reveals accuracy of data imputation using NNM and EM for all stations and various level of missingness. According to Table 7, it is shown that NNM is generally more accurate data imputation method compared to EM (except for CA0050 in set B). This is reflected by lower values for NNM for most of the cases. This may be due to its ability to predict missing data closer to actual data compared to EM.

Mean absolute percentage error (MAPE) of stations in Sabah for various missingness level.

## 4. CONCLUSION

Generally, it has been shown that NNM is better imputation method for data from all the monitoring stations in Sabah except CA0050. NNM works most efficient for CA0049 in Part A (RMSE<14.302, MAE<10.640, IA>0.819 and COD>0.586) and CA0042 in Part B (RMSE<10.722, MAE<7.526, IA>0.835 and COD>0.632). This may be due to missing data type of MAR. However, strong fluctuation which may be present in data from CA0050 and part B from CA0030 may cause NNM to impute data not as well as EM algorithm. This may be further confirmed by regression analysis for CA0050 (R>0.711 for part B). Evaluation of accuracy using MAPE reveals that NNM is more accurate imputation method for most cases (except for set B in CA0050). This shows that NNM can be used as data imputation for missing data found in dataset observed by stations in Sabah. Accurate data imputation is important for future research because this enables further analysis on air quality data to become more reliable.

## Acknowledgments

The authors would like to thank Universiti Malaysia Sabah for supporting this research by providing grant (SBK0324-2018, SGI0054-2018 and GUG0378-2018) and Department of Environment Malaysia for providing meteorological and pollutant data for research purpose.

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### Fig. 1.

Location of PM10 monitoring stations at urban and suburban areas (Kota Kinabalu, Tawau, Sandakan, Keningau, Labuan) in Sabah.

### Fig. 2.

Spatial distribution of estimated PM10 concentration in Sabah from 2007-2011 for (a) dry season (June-September), (b) wet season (November-March), (c) intermonsoon (April-May), and (d) intermonsoon (October) based on MODIS-AOD500 and meteorological variables (Kanniah et al., 2016).

### Fig. 3.

Scatter plot for imputation of data from CA0042 and CA0050 for part A and B at various missingness percentage. Blue indicates NNM, red indicates EM, while dashed line represents the point where predicted data equals observed data.

### Table 1.

Location of monitoring stations in Sabah.

Station ID Station name Latitude Longitude Altitude (m)
CA0030 SM Putatan, Kota Kinabalu 5.9804° N 116.0735° E 13
CA0039 Pejabat JKR Tawau, Tawau 4.2447° N 117.8912° E 12
CA0042 Pejabat JKR Sandakan, Sandakan 5.8394° N 118.1172° E 10
CA0049 SMK Gunsanad, Keningau 5.3374° N 116.1567° E 288
CA0050 Taman Perumahan MPL, Labuan 5.3441° N 115.2404° E 13

### Table 2.

Percentage of missingness as conducted by Noor et al. (2014).

Degree of complexity Percentage of missingness (%)
Small 5
10
Medium 15
25
Large 40

### Table 3.

Performance indicators for every station and missingness percentage for part A.

Station Missing-ness
(%)
Performance indicators
RMSE MAE IOA COD
NNM EM NNM EM NNM EM NNM EM
Remark: Data ranges from year 2003 to 2007
CA0030 5 18.130 17.161 11.765 11.699 0.760 0.649 0.495 0.509
10 17.022 16.864 11.279 11.728 0.782 0.646 0.536 0.505
15 16.887 16.672 11.422 11.715 0.784 0.651 0.540 0.503
25 16.862 16.205 11.496 11.488 0.782 0.660 0.538 0.505
40 17.362 16.412 11.745 11.504 0.769 0.660 0.521 0.506
CA0039 5 21.701 23.367 13.371 15.648 0.787 0.582 0.522 0.517
10 21.000 23.001 13.213 15.517 0.783 0.566 0.527 0.484
15 21.591 22.702 13.640 15.389 0.770 0.572 0.504 0.487
25 21.526 22.648 13.756 15.376 0.776 0.569 0.526 0.497
40 22.654 22.742 14.220 15.406 0.750 0.569 0.488 0.485
CA0042 5 15.712 17.525 10.841 11.761 0.804 0.511 0.595 0.370
10 15.393 16.923 10.609 11.637 0.801 0.530 0.586 0.397
15 15.229 16.543 10.588 11.574 0.795 0.544 0.577 0.407
25 14.930 16.151 10.506 11.510 0.798 0.556 0.585 0.428
40 15.328 16.313 10.824 11.656 0.792 0.553 0.574 0.425
CA0049 5 13.560 14.797 13.371 10.451 0.841 0.645 0.630 0.566
10 13.861 15.218 13.213 10.609 0.835 0.626 0.611 0.534
15 13.707 15.099 13.640 10.639 0.834 0.619 0.613 0.520
25 13.883 15.305 13.756 10.640 0.830 0.610 0.599 0.514
40 14.302 15.163 14.220 10.597 0.819 0.619 0.586 0.518
CA0050 5 14.937 13.258 10.666 10.095 0.719 0.676 0.482 0.473
10 15.685 13.314 10.856 10.093 0.702 0.665 0.451 0.467
15 15.552 13.161 10.818 9.953 0.698 0.664 0.453 0.464
25 15.251 13.266 10.752 9.903 0.711 0.663 0.469 0.471
40 15.239 13.351 10.843 9.957 0.707 0.661 0.468 0.467

### Table 4.

Performance indicators for every station and missingness percentage for part B.

Station Missing-ness
(%)
Performance index
RMSE MAE IOA COD
NNM EM NNM EM NNM EM NNM EM
Remark: Data ranges from year 2008 to 2012
CA0030 5 16.676 14.553 12.117 10.864 0.734 0.698 0.506 0.521
10 16.299 14.486 12.003 10.864 0.751 0.703 0.526 0.533
15 16.578 14.595 12.075 10.933 0.743 0.703 0.512 0.528
25 16.971 14.660 12.247 10.975 0.726 0.695 0.495 0.519
40 17.758 14.988 12.506 11.055 0.706 0.688 0.461 0.508
CA0039 5 13.996 18.965 9.867 15.145 0.860 0.666 0.661 0.535
10 14.383 18.737 9.977 15.062 0.846 0.672 0.629 0.531
15 14.365 18.913 9.994 15.164 0.849 0.668 0.647 0.528
25 14.602 19.104 10.187 15.258 0.852 0.669 0.654 0.522
40 15.484 18.984 10.753 15.246 0.830 0.673 0.632 0.530
CA0042 5 10.615 12.535 7.450 9.652 0.845 0.616 0.640 0.476
10 10.308 12.533 7.260 9.675 0.847 0.606 0.642 0.466
15 10.430 12.699 7.287 9.712 0.851 0.602 0.647 0.461
25 10.505 12.602 7.368 9.729 0.847 0.602 0.644 0.469
40 10.722 12.809 7.526 9.770 0.835 0.591 0.632 0.451
CA0049 5 18.255 17.987 9.867 12.430 0.756 0.529 0.457 0.400
10 16.754 17.404 9.977 12.274 0.780 0.551 0.492 0.428
15 16.966 18.046 9.994 12.457 0.777 0.530 0.486 0.399
25 16.771 18.225 10.187 12.574 0.780 0.521 0.495 0.394
40 17.564 18.143 10.753 12.629 0.758 0.523 0.462 0.396
CA0050 5 23.646 16.463 14.435 11.360 0.693 0.795 0.405 0.609
10 23.071 16.22 14.070 11.317 0.701 0.798 0.427 0.616
15 23.210 16.007 14.114 11.272 0.695 0.809 0.418 0.633
25 23.163 16.279 14.173 11.278 0.696 0.800 0.414 0.622
40 22.865 16.203 14.213 11.319 0.698 0.800 0.424 0.625

### Table 5.

Coefficient of correlation for dataset in Part A.

Missingness
(%)
Station
CA0030 CA0039 CA0042 CA0049 CA0050
NNM EM NNM EM NNM EM NNM EM NNM EM
Remark: Data ranges from year 2003 to 2007
5 0.593 0.569 0.633 0.575 0.653 0.406 0.714 0.604 0.524 0.363
10 0.624 0.547 0.626 0.535 0.648 0.429 0.707 0.580 0.504 0.507
15 0.626 0.552 0.606 0.539 0.639 0.438 0.704 0.561 0.497 0.504
25 0.622 0.555 0.613 0.541 0.644 0.456 0.698 0.553 0.513 0.514
40 0.602 0.560 0.575 0.537 0.634 0.449 0.680 0.558 0.506 0.512

### Table 6.

Coefficient of correlation for dataset in Part B.

Missingness
(%)
Station
CA0030 CA0039 CA0042 CA0049 CA0050
NNM EM NNM EM NNM EM NNM EM NNM EM
Remark: Data ranges from year 2008 to 2012
5 0.544 0.577 0.746 0.558 0.721 0.493 0.594 0.386 0.498 0.711
10 0.570 0.587 0.723 0.566 0.725 0.487 0.628 0.412 0.506 0.716
15 0.560 0.586 0.728 0.560 0.732 0.485 0.622 0.386 0.498 0.729
25 0.533 0.571 0.732 0.565 0.724 0.490 0.625 0.369 0.500 0.723
40 0.506 0.564 0.695 0.571 0.704 0.473 0.594 0.363 0.501 0.723

### Table 7.

Mean absolute percentage error (MAPE) of stations in Sabah for various missingness level.

Set Missing-ness
(%)
Station
Kota Kinabalu Tawau Sandakan Keningau Labuan
NNM EM NNM EM NNM EM NNM EM NNM EM
A 5 35.771 38.619 25.091 27.545 33.003 36.986 26.217 31.333 37.707 39.461
10 34.874 39.585 24.925 27.759 32.558 37.109 25.916 31.282 38.180 38.842
15 35.260 39.367 26.160 27.763 32.853 37.231 25.717 31.038 38.274 38.285
25 35.835 38.428 26.496 27.745 32.794 37.773 25.935 31.108 37.627 37.652
40 36.051 37.932 27.407 27.668 33.795 37.859 26.467 30.888 37.645 37.812
B 5 42.717 44.935 28.481 59.879 25.373 40.454 27.214 42.656 40.381 37.333
10 43.452 46.053 28.743 59.450 25.204 41.661 26.583 43.593 39.701 37.232
15 43.741 45.783 29.204 59.890 25.409 41.824 26.510 43.857 39.440 36.847
25 44.431 46.577 30.007 60.157 25.918 42.443 26.655 43.965 39.875 36.972
40 45.364 47.055 32.239 60.652 26.601 42.348 27.922 44.606 40.546 37.309