[[abstract]]Gender parity issues have been discussed widely in previous literature. While trend analysis for this phenomenon is still very limited. This study focuses on the effect of system expansion on faculty gender parity by using transfer function and ARIMA to tackle the series data. Gender parity index was transformed by Becker’s discrimination coefficient (D) to detect the patterns of gender parity in the selected higher education system. To predict the future trend, the ARIMA (autoregressive integrated moving average) was used to build the fittest model to interpret the trends of D in next decade. The findings display the higher education system still favored male faculty, whereas following the post-expansion in next decade, the gender parity will reduce its discrepancy. This study provides an example to tackle the similar issue in different higher education settings.[[notice]]補正完

Chang, Dian-Fu

Gender parity issues have been discussed widely in previous literature. While trend analysis for this phenomenon is still very limited. This study focuses on the effect of system expansion on faculty gender parity by using transfer function and ARIMA to tackle the series data. Gender parity index was transformed by Becker’s discrimination coefficient (D) to detect the patterns of gender parity in the selected higher education system. To predict the future trend, the ARIMA (autoregressive integrated moving average) was used to build the fittest model to interpret the trends of D in next decade. The findings display the higher education system still favored male faculty, whereas following the post-expansion in next decade, the gender parity will reduce its discrepancy. This study provides an example to tackle the similar issue in different higher education settings.補正完

Tamkang University Institutional Repository

ICIC Express LettersPart B: Applications ICIC International c⃝2020 ISSN 2185-2766Volume 11, Number 3, March 2020 pp. 221–227DETERMINING SYSTEM EXPANSION ON FACULTY GENDERPARITY BY USING ARIMADian-Fu Chang1 and Hui Hu2,∗1Graduate Institute of Educational Policy and Leadership2Doctoral Program of Educational Leadership and Technology ManagementTamkang UniversityNo. 151, Yingzhuan Road, Tamsui District, New Taipei City 25137, Taiwan140626@mail.tku.edu.tw; ∗Corresponding author: 806760095@s06.tku.edu.twReceived September 2019; accepted December 2019Abstract. Gender parity issues have been discussed widely in previous literature. Whiletrend analysis for this phenomenon is still very limited. This study focuses on the effectof system expansion on faculty gender parity by using transfer function and ARIMA totackle the series data. Gender parity index was transformed by Becker’s discriminationcoefficient (D) to detect the patterns of gender parity in the selected higher education sys-tem. To predict the future trend, the ARIMA (autoregressive integrated moving average)was used to build the fittest model to interpret the trends of D in next decade. The find-ings display the higher education system still favored male faculty, whereas following thepost-expansion in next decade, the gender parity will reduce its discrepancy. This studyprovides an example to tackle the similar issue in different higher education settings.Keywords: ARIMA, Faculty members, Gender parity, Higher education, Time series1. Introduction. According to the 2017 data of the United Nations Educational, Scien-tific and Cultural Organization (UNESCO), the gross entrance ratios (GERs) are 86% inFinland, 91% in Spain, and 93.78% in Korea [1]. The GER is usually as an indicator toreflect the development of a higher education. This indicator also relates to enrollmentor participation in higher education. Typically, the higher education systems followedrational process to extend their participation and might cause structure change withinthe systems. Previous studies have shown that higher education expansion will trans-form the student gender parity. For example, when the higher education system goesinto the later stage of gross entrance ratio (GER) 15%-50% or over 50%, the numberof female students has gradually become greater than that of male students [2,3]. Fur-thermore, women are persistently under-represented in technology and engineering, butover-represented in other STEM (science, technology, engineering and mathematics) fields[4]. This phenomenon is also displayed in other countries [5,6]. This trend illustrates whenstudent number increases in higher education, the system is going to favor female stu-dents. Most of previous studies have focused on the gender parity in student groups;however, the gender pattern of faculty groups is still unclear. This phenomenon might beinterpreted by the current studies that only focused on the specific gender issues in highereducation settings [7-10]. In this study, we tried to realize whether the system expansionhas ensured faculty increasing or changed the patterns of faculty gender? We found thisissue with long-term trend has been discussed very limited in current research literature.The finding will provide meaningful information for related policy makers.Moreover, series data have been mining for different fields and provides a lot of forecast-ed experiences. For example, autoregressive integrated moving average (ARIMA) modelshave been applied for various fields in higher education settings, while the system itselfDOI: 10.24507/icicelb.11.03.221221222 D.-F. CHANG AND H. HUwith the issues still did not be addressed properly by using the predicted model. Thisstudy aims to realize the faculty gender pattern change by using ARIMA models to tacklethe series data. We tried to transform the gender parity index for faculty in the targethigher education system. The data transformation and ARIMA model could be a newapproach in this field. Given this purpose, this study selected Taiwan as a research targetto tackle the faculty gender parity issue in the system. Specifically, this study tries toanswer the following research questions:a. What trends are shown in gender of faculty with the system expansion?b. Has there been reduction in faculty gender discrepancy in the expanded higher edu-cation system?c. What trend regarding faculty gender parity is likely in the next decade?The result will provide two patterns of faculty gender in previous and future trends inthe selected higher education system. The structure of this paper is as follows. First,the method section addresses the characteristics of series data and the ARIMA models.Then, the results will be displayed and made further discussions. Finally, the conclusionand implication will be drawn.2. Method. In this section, we define the crucial terms in this study, determine the crosscorrelation of both series, and build the fittest ARIMA model with Becker’s discriminationcoefficient (D) to predict the faculty gender parity in next decade.2.1. Definition of terms. System expansion refers to open enrollment policy to widenthe participation in higher education system. According to data from the UNESCOInstitute for Statistics (2018), the GER in high income countries moved to a universalstage in 1993. Some countries reached 75% in 2011, while the GER in most of the middle-income countries moved to the mass stage in 2001 [4]. In our research target, the GERin this system increased from 15% (1976) to 50% (1999) during these 23 years. Whilethe GER up to 85% happened in 2007, the system only spent another 8 years to reachthe ceiling of GER [2]. Faculty gender parity refers to the parity working opportunity formale and female faculty in higher education institutions. In this study, the parity indexwill be calculated by using Becker’s D based on annual data from Ministry of Education,Taiwan.2.2. Testing cross correlation with enrollment and faculty members. This studyconsidered a cross correlation to determine the relationship between two series variablescontemporaneously and at various lagged values. Cross correlations help us understandif two variables are related to each other and, if so, whether movement in one variabletends to precede or follow movement in the other. Typically, the cross correlation function(CCF) is applying for identifying lags of the x-variable that might be useful predictors ofyt [5,6]. Pre-whitening solves this problem by removing the autocorrelation and trendswith related series data SPSS can help to get CCF with its cross correlation command inforecasting. The CCF is defined as the set of correlations between xt+h and yt for h = 0,±1, ±2, ±3, and so on. A negative value for h is a correlation between the x-variable ata time before t and the y-variable at time t. For instance, consider h = −2. The CCFvalue would give the correlation between xt−2 and yt.• When one or more xt+h with h negative, are predictors of yt, it is sometimes saidthat x leads y.• When one or more xt+h, with h positive, are predictors of yt, it is sometimes saidthat x lags y.2.3. Data transformation. This study selected the data from the Ministry of Educationas an example to realize the phenomenon in higher education settings [7,8]. In this specificfield, the data were collected from 1968 to 2018 based on annual basis. Gender parity inICIC EXPRESS LETTERS, PART B: APPLICATIONS, VOL.11, NO.3, 2020 223faculty members was defined as the Becker’s discrimination coefficient. The D is definedas follows [9,10]:Di = (FMi/FFi)− 1where, FM represents the male faculty, FF represents the female faculty in the highereducation, and i represents the series data collection period from 1968 to 2017. Theinterpretation of D will follow the following rules:• An increase in the calculated D implies that the system favors male faculty;• The calculated D being negative means that system favors female faculty;• A calculated D of zero or near zero represents equal opportunity for female and malefaculty in the education system.2.4. Building ARIMA model. The estimated patterns of faculty gender parity wereconducted using ARIMA (autoregressive integrated moving average) model for furtherinterpretation. Generally, in ARIMA model, the basic series data needed 50 periods ormore. The selected data set with 51 periods fit the criterion. The fittest model wasselected to interpret the data and the robustness of the forecasting model was evaluatedfor estimation from 2019-2028. This study followed the ARIMA(p, d, q) model buildingprocess as follows: 1) prepare target data to detect the data set is stationary or nonsta-tionary series; 2) identify potential forecast models; 3) check the ACF (autocorrelationfunction)/PACF (partial autocorrelation function) of the residuals; and 4) forecast theseries in next decade [11-14]. A non-seasonal ARIMA(p, d, q) model, where: p is thenumber of autoregressive terms, d is the number of non-seasonal differences needed forstationarity, and q is the number of lagged forecast errors in the prediction equation. D-ifferenced series data provides more stationary types for forecasting, typically, two timesdifference is enough [15]. In this study, inspection of the ACF of a time series was used todetermine whether a series is stationary or will require differencing [13,14]. The ACF andPACF should be considered together. For example, AR models have theoretical PACFswith non-zero values at the AR terms in the model and zero values elsewhere. The esti-mation of parameter for D will be presented to check the coefficient is significant. In thisstudy, Box-Pierce Chi-square statistics were used to determine whether the model metthe assumptions that the residuals were independent [16]. The calculations were listed asfollows [16,17]:Q∗(K) = (n− d) · (n− d+ 2) ·K∑l=1(n− d− l) · r2l (â)where, n is the sample size, d is the degree of non-seasonal differencing used to transformthe original series to a stationary one, r2l (â) is the sample autocorrelation at lag l for theresiduals of the estimated model, K is the number of lags covering multiples of seasonalcycles, e.g., 12, 24, 36, . . . , for yearly data.In this process, we check the criteria for a white noise test on time series are describedas follows: If the number is classified as white noise, thena. the series averages are fixed;b. the series variance is fixed; andc. the series self-covariance is 0; that is, in this period, the last issue of the series is notrelated.3. Results. Following the cross correlation function, ARIMA model selection, and fore-casting, we present the results with related tables and figures.224 D.-F. CHANG AND H. HU3.1. Cross correlation function between enrollment and faculty members. Table1 displays the lag 7 to lag −7 with higher cross correlation; it implies the enrollmentand faculty members with relationship contemporaneously and at various lagged values.Faculty members increasing is related to the enrollment increasing. Figure 1 demonstratesthe CCFs are significant. The effect of higher education expansion will impact on facultymembers increasing. While how to determine the effect of expansion on faculty genderparity that might be transformed? It needs detecting the male and female faculty datato further interpretation. The next section will address the details of series D in ARIMAmodel.Table 1. Cross correlation function with enrollment and faculty membersLag −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7Cross correlation 0.357 0.341 0.347 0.386 0.439 0.515 0.603 0.673 0.647 0.659 0.609 0.592 0.543 0.490 0.420Standard error 0.152 0.151 0.149 0.147 0.146 0.144 0.143 0.141 0.143 0.144 0.146 0.147 0.149 0.151 0.152Figure 1. Cross correlation function between enrollment and facultymembers from 1968 to 2018Table 2. Selecting ARIMA models for predicting DPredict D AR MA Ljung-Box SelectionARIMA(1, 2, 1) ⋆ • •ARIMA(1, 1, 1) • • • }ARIMA(1, 1, 2) • × ×Note. • = excellent, ⋆ = fair, × = unacceptable.3.2. Selecting ARIMA models. Based on one difference with the D series, the Minitabdisplays the ARIMA(1, 1, 1) is the fittest model, see Table 2. The ACF, PACF, andmodified Box-Pierce (Ljung-Box) Chi-square statistic all work well in ARIMA(1, 1, 1)model, see Table 3 and Figure 2. The coefficients of AR(1) = 0.95 (p = .00) and MA(1) =0.60 (p = .00) are significant at .05 level. In Box-Pierce (Ljung-Box) Chi-square statisticICIC EXPRESS LETTERS, PART B: APPLICATIONS, VOL.11, NO.3, 2020 225Table 3. Final estimates of parameters and modified Box-Pierce (Ljung-Box) Chi-square statisticType Coef SE Coef t-value p-value Lag 12 24 36 48AR(1) 0.95 0.07 14.22 0.00 Chi-square 6.59 10.15 13.90 20.41MA(1) 0.60 0.15 4.10 0.00 DF 9 21 33 45Constant −0.003 0.003 −0.97 0.34 p-value 0.679 0.977 0.999 0.999Figure 2. ACF and PACF for ARIMA(1, 1, 1)test, we check the predicted series values with the number of lags 12, 24, 36, and 48 whichare classified as white noise (p > .05). The proposed ARIMA(1, 1, 1) model is robust. Thisstudy also applies two differences with the D series, the result reveals ARIMA(1, 2, 1) didnot work well due to its low coefficient of AR(1), see Table 2.226 D.-F. CHANG AND H. HU3.3. Projecting faculty gender parity (D). This study conducts ARIMA(1, 1, 1)model to predict the D in next decade. The result displays in Figure 3. Based onthe prediction trend, the D will decline steadily in future. It implies the expanded highereducation system will create a friendly environment for female faculty. Table 4 reveals,the forecast D will decrease from 0.734 in 2019 to 0.432 in 2028. The discrepancy ofgender has shown diminishing.Figure 3. Time series plot for D from 1968 to 2028Table 4. Forecasts of D from 2019 to 2028Year Forecast95% LimitsLower Upper2019 0.734 0.629 0.8382020 0.706 0.530 0.8822021 0.677 0.428 0.9272022 0.646 0.320 0.9722023 0.614 0.208 1.0192024 0.580 0.092 1.0682025 0.545 −0.028 1.1182026 0.509 −0.151 1.1682027 0.471 −0.278 1.2192028 0.432 −0.406 1.2704. Conclusion. This study conducts cross correlation function to tackle the series rela-tionships in higher education expansion phenomenon. Becker’s discrimination coefficientworks well in this study to interpret the faculty gender parity transformation. Accordingto the predictions with ARIMA model, in the next decade, the system may still favormale faculty in higher education institutions. However, according to the D, the situationis improving under the system development. Moreover, the trends reveal that gaps infaculty gender parity will decrease in the next decade.This paper provides an example of an effective approach to addressing gender parity inan expanding higher education system. Although the quantitative approach was limitedICIC EXPRESS LETTERS, PART B: APPLICATIONS, VOL.11, NO.3, 2020 227by the data set and transform model, the explanation of the trends provides a longitudinalperspective for reviewing the effect of expanded higher education on our concern issues.For further work, this paper proposes conducting cross-country comparisons with theresearchers in the community to address similar issues.REFERENCES[1] UNESCO Institute for Statistics, UIS Statistics – Gross Enrolment Ratio by Level of Education,http://data.uis.unesco.org/, 2018.[2] D.-F. 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DETERMINING SYSTEM EXPANSION ON FACULTY GENDER PARITY BY USING ARIMA

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DETERMINING SYSTEM EXPANSION ON FACULTY GENDER PARITY BY USING ARIMA

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