Longitudinal Data Analysis - Essay Example

? Longitudinal Data Analysis Longitudinal Data Analysis Introduction In this paper, longitudinal data which has been collected over a period of time from a sample of households and individuals is subjected to different statistical models to form a basis for acceptance or rejection of a hypothetical relationship set out for the study. In the current research paper, the relationship between education qualifications attained by individuals and their financial positions is investigated. This relationship has been selected for investigation on the basis of previous studies such as one by Maani (2002) which clearly indicates that as the number of individuals dropping out from college in Maori increased, which suggested comparatively low level of qualifications attained by individuals, there was a fall in the income earned by individuals living in this area of New Zealand and hence their financial position is the outcome of their attainment of education qualification. In the same way, the present study is aimed at using different statistical models and graphs to explore the trend in the selected variables and predict the relationship between them. Furthermore, the results are presented keeping in view the ethnic background of individuals who participated in the survey. Objective: The objective of the study is to investigate the relationship between the level of qualifications attained by individuals and their financial position based on the ethnical background of individuals’ living in Britain over a period from 1990 to 2001 who took part in the BHPS survey. Research Questions: 1. What are the descriptive trends of education qualifications amongst individuals belonging to different ethnical backgrounds? 2. What are the descriptive trends of the financial position amongst individuals belonging to different ethnical backgrounds? 3. What is the relationship between the level of educational qualifications and financial position of individuals in Britain over a period of time from 1990 to 2001? Longitudinal Data The data selected for evaluating the relationship between educational qualifications and financial position individuals in Britain is extracted from the survey data collected through The British Household Panel Survey (BHPS) for a period of eleven years’ from 1991 to 2001. Since, the data is of longitudinal nature therefore it would be appropriate to use weighted data for adjusting unweighted data over the period of consideration. Weighting of individual data has been made for non-response of individuals within households i.e. same individuals were missing to participate in later waves of data collection. Individuals’ response data weights have been collected for 12 years from a variable – xLRWGHT included in the data set. Selection of Variables In order to study the relationship between educational qualifications and income levels of individuals the following variables have been identified and selected from BHPS dataset. Dependent Variable: The dependent variable selected for the study is the financial position of individuals. The associated variable from the dataset is ‘xfisit’ from BHPS dataset for 12 waves of data collected. Independent Variable (Covariate): The independent variable selected for the study is the highest education qualification. The associated variable from the dataset is ‘xiqfedhi’ from BHPS dataset for 12 waves of data collected. Fixed Variable: The analysis is performed on the basis of ethnic background of individuals. For this purpose, variable ‘arace’ has been selected which is described as ethnic group membership. There are nine subsets under this variable including White, Black-Carib, Black-African, Black-Others, Indian, Pakistani, Chinese, Bangladeshi, and Other Ethnic Groups. Hypotheses Establishment: In this study the relationship between education qualifications and financial position of individuals over a period of 12 years is investigated for testing out the following research hypothesis: H0: There is no significant relationship between educational qualifications and financial position amongst individuals from different ethnic backgrounds. H1: There is a significant relation between educational qualifications and financial position individuals from different ethnic backgrounds. Methodology: The methodology that has been adopted for the current study is aimed at providing a detailed examination of the data that has been collected through BHSP for providing vital information regarding education qualifications and financial position recorded amongst individuals belonging to different ethnic backgrounds. This is carried out using Explore and Cross Tab options available in SPSS for descriptive statistics. The current study also uses correlation matrix and multiple linear regression model for analysing the relationship between dependent and independent variable. The multiple regression model can be represented using the following linear equation: ?: ?0 + ?1*x1 + ?2*x2 Where ? = Mean value of dependent variable xi = Independent variables ?i = Variable Coefficient In this study, the fixed effects model investigates the impact of two variables including education qualification and ethnic group membership on individual annual income level. For this purpose the data is restructured to provide instances of data based on ethnic group memberships creating an index which represents 12 waves of data collection over a period from 1990 to 2001 (SPSS Inc., 2005) Descriptive Statistics Cross Tabulation The following three-way cross tabulation table provides the descriptive analysis of two variables that are highest level of education qualifications and the financial position of individuals based on the ethnic division. As it has been indicated that there are 9 divisions of the sample population are made on the basis of individuals’ ethnic backgrounds therefore from the table below it can be seen that individuals belonging to any ethnic background having higher, first, or professional qualifications including nursing and teaching have responded positively that they are living comfortably. It is also noted that a major proportion of the sample population belonging to the ethnic background ‘White’ did not have any form of qualification but yet results are mix as individuals have responded differently and somewhat in proportion to different options available to them. Based on the totals of each ethnic group it could be suggested that two ethnic groups including Black-Carib and Pakistanis appear to have the lowest proportion of individuals who have responded positively that they are living comfortably. Thus, from the cross tabulation analysis it could be inferred that individuals who have attained higher qualifications are in a better financial position. Highest educational qualification * Financial situation * Ethnic group membership Crosstabulation Count Ethnic group membership Financial situation Total Don't know Living comfortably Doing alright Just abt getting by Finding it quite difficult Finding it very difficult White Highest educational qualification Higher Degree 1 763 444 212 57 18 1495 First Degree 6 2737 2154 1130 358 129 6514 Teaching QF 0 1097 809 407 82 32 2427 Other Higher QF 17 5043 5583 3319 798 297 15057 Nursing QF 1 546 484 357 77 23 1488 GCE A Levels 5 2356 3082 1957 507 176 8083 GCE O Levels or Equiv 8 4282 5645 4157 962 396 15450 Commercial QF, No O Levels 2 871 923 872 161 77 2906 CSE Grade 2-5,Scot Grade 4-5 4 552 1011 912 195 114 2788 Apprenticeship 0 605 581 657 110 69 2022 Other QF 4 99 175 142 28 20 468 No QF 31 6199 6573 8596 1666 896 23961 Still At School No QF 2 10 13 9 0 2 36 Total 81 25160 27477 22727 5001 2249 82695 Black-Carib Highest educational qualification Higher Degree 0 3 4 5 3 1 16 First Degree 1 10 16 12 6 1 46 Teaching QF 0 0 2 4 0 0 6 Other Higher QF 1 9 48 37 2 4 101 Nursing QF 0 4 7 17 5 2 35 GCE A Levels 1 0 7 16 1 2 27 GCE O Levels or Equiv 0 8 19 10 2 0 39 Commercial QF, No O Levels 0 1 7 2 0 1 11 CSE Grade 2-5,Scot Grade 4-5 0 0 0 1 1 0 2 Apprenticeship 0 0 3 2 1 0 6 Other QF 0 0 1 1 1 0 3 No QF 0 4 24 75 11 13 127 Total 3 39 138 182 33 24 419 Black-African Highest educational qualification Higher Degree 4 18 4 6 2 34 First Degree 5 17 5 3 3 33 Teaching QF 1 2 5 1 1 10 Other Higher QF 3 24 29 10 7 73 Nursing QF 2 0 2 0 0 4 GCE A Levels 1 6 6 8 5 26 GCE O Levels or Equiv 2 3 7 11 3 26 Commercial QF, No O Levels 0 0 3 0 0 3 CSE Grade 2-5,Scot Grade 4-5 1 0 0 2 0 3 Other QF 0 1 2 2 6 11 No QF 0 3 4 6 17 30 Total 19 74 67 49 44 253 Black-Other Highest educational qualification Higher Degree 10 1 1 0 0 12 First Degree 8 8 2 0 3 21 Teaching QF 1 6 5 3 0 15 Other Higher QF 4 8 6 0 2 20 Nursing QF 0 0 1 1 0 2 GCE A Levels 4 3 10 7 5 29 GCE O Levels or Equiv 0 6 5 1 0 12 Commercial QF, No O Levels 0 1 0 0 1 2 CSE Grade 2-5,Scot Grade 4-5 0 5 7 0 0 12 No QF 1 4 5 12 10 32 Total 28 42 42 24 21 157 Indian Highest educational qualification Higher Degree 0 14 19 3 0 0 36 First Degree 0 71 47 32 4 0 154 Teaching QF 0 4 2 6 0 0 12 Other Higher QF 0 38 83 64 26 12 223 Nursing QF 0 11 14 2 0 0 27 GCE A Levels 0 23 35 23 3 3 87 GCE O Levels or Equiv 0 29 46 35 9 5 124 CSE Grade 2-5,Scot Grade 4-5 0 3 7 4 10 1 25 Other QF 0 6 29 25 13 1 74 No QF 2 6 26 55 38 45 172 Still At School No QF 0 0 0 1 0 0 1 Total 2 205 308 250 103 67 935 Pakistani Highest educational qualification Higher Degree 0 0 5 2 0 0 7 First Degree 0 1 8 4 4 0 17 Other Higher QF 0 3 26 18 3 2 52 GCE A Levels 0 3 3 2 0 1 9 GCE O Levels or Equiv 0 1 4 6 4 1 16 Commercial QF, No O Levels 0 1 0 0 0 0 1 CSE Grade 2-5,Scot Grade 4-5 0 2 14 16 6 3 41 Other QF 1 0 3 8 0 2 14 No QF 0 9 28 40 26 22 125 Total 1 20 91 96 43 31 282 Bangladeshi Highest educational qualification First Degree 0 1 6 0 1 8 Other Higher QF 2 0 0 0 0 2 GCE A Levels 0 3 0 0 0 3 GCE O Levels or Equiv 1 1 1 0 0 3 No QF 4 8 9 9 0 30 Total 7 13 16 9 1 46 Chinese Highest educational qualification Higher Degree 9 9 4 0 0 22 First Degree 9 7 10 2 1 29 GCE A Levels 1 4 0 0 0 5 GCE O Levels or Equiv 3 11 1 0 0 15 Commercial QF, No O Levels 1 6 1 1 0 9 No QF 0 1 0 0 0 1 Total 23 38 16 3 1 81 Other ethnic grp Highest educational qualification Higher Degree 13 12 13 1 1 40 First Degree 32 59 36 15 3 145 Teaching QF 0 9 0 1 0 10 Other Higher QF 16 32 28 13 2 91 Nursing QF 5 0 6 0 0 11 GCE A Levels 23 18 23 3 2 69 GCE O Levels or Equiv 8 36 47 10 9 110 Commercial QF, No O Levels 1 1 0 0 0 2 CSE Grade 2-5,Scot Grade 4-5 3 3 7 1 0 14 Other QF 10 3 3 1 1 18 No QF 22 29 37 9 10 107 Total 133 202 200 54 28 617 Total Highest educational qualification Higher Degree 1 816 512 244 67 22 1662 First Degree 7 2873 2317 1237 392 141 6967 Teaching QF 0 1103 830 427 87 33 2480 Other Higher QF 18 5118 5804 3501 852 326 15619 Nursing QF 1 568 505 385 83 25 1567 GCE A Levels 6 2411 3161 2037 529 194 8338 GCE O Levels or Equiv 8 4334 5771 4269 999 414 15795 Commercial QF, No O Levels 2 875 938 878 162 79 2934 CSE Grade 2-5,Scot Grade 4-5 4 561 1040 947 215 118 2885 Apprenticeship 0 605 584 659 111 69 2028 Other QF 5 115 212 181 45 30 588 No QF 33 6245 6696 8821 1777 1013 24585 Still At School No QF 2 10 13 10 0 2 37 Total 87 25634 28383 23596 5319 2466 85485 Table 1: Descriptive Analysis of Educational Qualifications based on Ethnic Differences The above results are graphically represented on the basis of the differences in the ethnic backgrounds of individuals. The stacked bar chart provided above clearly supports the findings of cross tabulation as the smallest proportion of ‘living comfortably’ belongs to Black-Carib and Pakistanis. This graph indicates that a major proportion of Bangladeshi do not have any qualification and the Chinese individuals hold largest proportion of Higher Degree as compared other individuals from other ethnic backgrounds. Correlation Matrix The correlation between three variables identified for this study is presented in the following matrix. This matrix has been derived using Spear Correlations WeightedFinancialPosition Ethnic group membership WeightedEducation Spearman's rho WeightedFinancialPosition Correlation Coefficient 1.000 .040** .582** Sig. (2-tailed) . .000 .000 N 87992 87922 87707 Ethnic group membership Correlation Coefficient .040** 1.000 -.038** Sig. (2-tailed) .000 . .000 N 87922 118716 87668 WeightedEducation Correlation Coefficient .582** -.038** 1.000 Sig. (2-tailed) .000 .000 . N 87707 87668 87744 **. Correlation is significant at the 0.01 level (2-tailed). The table indicates positive correlation between the financial position of individuals and their ethnic background and highest educational qualification obtained by them. However, the magnitude of the relationship between the financial position and ethnic background is weak as the value is close to 0 (i.e. .040). On the other hand, it can be stated that the magnitude of the relationship between the financial position and ethnic background is moderate (i.e. .582). Both relationships are found to be significant at the confidence level of 0.01. Multiple Linear Regression For this stage of analysis, multiple regression analysis using enter method has been used. The dependent variable is set as the weighted financial condition of individuals and independent variables include the weighted education qualification and ethnic backgrounds of individuals as indicated in the following table. Variables Entered/Removeda Model Variables Entered Variables Removed Method 1 Ethnic group membership, Highest educational qualificationb . Enter a. Dependent Variable: Financial situation b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .569a .323 .323 1.19305 a. Predictors: (Constant), Ethnic group membership, WeightedEducation The above table indicates the coefficient of determination R2 is .323 that implies that the multiple linear regression that is able to explain only 32.3% of the total variations found in the sample of 87,636 individuals selected for the BHSP survey. This could be considered as a small percentage however due to the complexity of factors affecting each other and the way in which they have been collected over a long period of time this value of coefficient of determinant could be considered as sufficient for the results presented in this report. It is understood that the coefficients obtained for each variable through the use of the multivariate regression model actually predict the impact of change in the value of the variable by holding the values of the other variables constant as it can be noted that in the regression performed in this report Ethnic group membership is set as a constant. This implies that the model is predicting the change in the financial position of individuals having various ethnic backgrounds due to change in the highest education qualification. ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 59630.150 2 29815.075 20946.893 .000b Residual 124735.170 87634 1.423 Total 184365.321 87636 a. Dependent Variable: WeightedFinancialPosition b. Predictors: (Constant), Ethnic group membership, WeightedEducation From the above ANOVA table it can be seen that out of the total variations as indicated by sum of squares is 184365.321 and the regression model is been able to explain 32.3% or 59630.15 of these variations whereas the residual is 124735.17. Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) .795 .009 93.505 .000 WeightedEducation .159 .001 .567 204.013 .000 Ethnic group membership .097 .004 .060 21.669 .000 a. Dependent Variable: WeightedFinancialPosition The above table indicates that the intercept is .795. The coefficients of slope are obtained as ?1: .159 (Highest educational qualification) and ?2: .097 (Ethnic group membership). This implies that there is a positive relationship between the values assigned to different ethnic backgrounds and also there is a positive relationship between the highest educational qualification and financial position. This implies that if individuals move up the educational qualifications then they are likely to experience better financial position as compared to individuals with low level or no education. On the basis of these results the following regression equation is achieved: Financial Position: 1.776 + .159 * Highest educational qualification + .097 * Ethnic group membership. Moreover, the table also indicates that the significance value p Read More