The Use of Exploratory Factor Analysis in Secondary Research: the Case of Motivation for Learning the Lithuanian Language by 8th Grade Students

The article deals with the use of exploratory factor analysis in quantitative secondary research. Exploratory factor analysis helps to find a theoretical background in the data of educational research. The way of proceeding the data in quantitative secondary research can be described as follows: data − exploratory factor analysis – theoretical background of research – interpretation of the data of secondary analysis. The article focuses on the phenomenon of motivation for learning the Lithuanian language by 8th grade students on the basis of the data of national research (2012). Exploratory factor analysis revealed the components of intrinsic motivation for learning the Lithuanian language. The questions Do you like Lithuanian language lessons; Are you interested in writing assignments at Lithuanian language lessons; Are you gifted in the Lithuanian language; Are you interested in reading texts in Lithuanian lessons are related with the factor of intrinsic motivation. The variables You are learning the Lithuanian language because you need to get a wellpaid job; You are learning the Lithuanian language because it is important to obtain an interesting job; You are learning the Lithuanian language, because it is important to get entry to a higher school; the Lithuanian language is important to learn other subjects have high factor loadings on another factor, namely extrinsic motivation.


Introcuction
In educational research, quantitative analysis refers to educational sciences that aim at understanding or predicting behavior or events through the use of mathematical measurements, as well as statistical modeling and research.The aim of quantitative analysis is to represent a given educational reality in terms of numerical value.In order to transmit educational reality into numeric value, it is important to perform the process operationalization."The process of operationalizing a questionnaire is to take a general purpose or set of purposes and turn these into concrete, researchable fields about which actual data can be gathered" (Cohen, Manion, & Morison, 2007, p. 318).In quantitative educational research, the general purposes of a questionnaire must be clarified and then translated into a specific, concrete aim or a set of aims.The theoretical background is important in the process of operationalization.This theoretical background is important in the process of explanation of quantitative research data.Wilson and McLean (1994, p. 8-9) suggest an approach "which is to identify the research problem, then to clarify the relevant concepts or constructs, then to identify what kinds of measures (if appropriate) or empirical indicators there are of these, i.e. the kinds of data required to give the researcher relevant evidence about the concepts or constructs, e.g.their presence, their intensity, their main features and dimensions" (Cohen, Manion, & Morison, 2007, p. 320).
"Secondary analysis is a practice of analyzing the data that have already been gathered by someone else, often for a distinctly different purpose" (Crossman, 2016).According to Crossman, secondary analysis as a research method, "saves both time and money and avoids unnecessary duplication of research effort".Secondary analysis is usually contrasted with primary analysis, which is an analysis of the data independently collected by a researcher.Scientists who carry out secondary analysis do not know the process of operationalization of the primary research.In the secondary quantitative research, it is important to determine what the theoretical basis of the primary research is.
Examples are the studies in which questionnaires consisting of a lot of questions (variables) are used, and the studies in which mental ability is tested via several subtests, like verbal skills tests, logical reasoning ability tests, etc (Darlington, 2004).It gives the possibility to receive a big amount of data from different areas of educational practice.In the secondary quantitative research, it is important to determine what the theoretical basis of primary research is.It is difficult to establish a theoretical framework of a large qualitative database."It is not always clear how data were collected, why certain types of data were collected while others were not, or whether any bias was involved in the creation of tools used to collect the data.Polls, questionnaires, and interviews can all be designed to result in pre-determined outcomes" (Crossman, 2016).The exploratory factor analysis can be used for finding out of theoretical background of primary research.factor analysis attempts to bring intercorrelated variables together under more general underlying variables.The goal of factor analysis is to reduce "the dimensionality of the original space and to give an interpretation to the new space, spanned by a reduced number of new dimensions which are supposed to underlie the old ones" (Rietveld & Van Hout, 1993, p. 254), or to explain the variance in the observed variables in terms of underlying latent factors" (Habing, 2003, p. 2).
In the national or international (TIMSS, PISSA) research, the field of questionnaire design is vast.Data sets are never fully used and the data re-used for new purposes.The problem of our research is how to adapt exploratory factor analysis in the secondary analysis of the national research.
The aim of the research is to reveal the possibility of exploratory factor analysis of school students' motivation for learning the Lithuanian language on the basis of the national research data.

Methodology
The secondary analysis of schools students' motivation for learning the Lithuanian language was carried out on the basis of the data of the national research (2012) on 8 th grade students.The questions about the motivation for learning the Lithuanian language (Table 1) were included into the questionnaire for eighth grade students (Questionnaire about the Lithuanian language for 8 th grade students, 2012).The questionnaire contained a group of questions (L1) related to the motivation for learning the Lithuanian language.Exploratory factor analysis (EFL) of questions from group L1 was completed.
EFA allowed to reduce the data about the motivation for learning the Lithuanian language (You like Lithuanian language lessons L1a; You are gifted for the Lithuanian language L1b; You are interested in reading texts in Lithuanian lessons L1c; You are interested in writing assignments at Lithuanian language lessons L1d; the Lithuanian language is important for learning other subjects L1e; You are learning the Lithuanian language because it is important to obtain entry to a higher school L1f; You are learning the Lithuanian language because it is important to obtain an interesting job L1g; You are learning the Lithuanian language because you need to get a well-paid job L1h) to a lower number of unobserved variables -factors.A priori assumption was that any indicator might be associated with any factor.All observed variables of questions in group L1 can be associated with the latent variable -different levels of motivation for learning Lithuanian: a motivation, extrinsic motivation, intrinsic motivation (Ryan & Deci, 2002).
The national student achievement tests were selected on the basis of random samples of students.The sampling principle is a nested random sample of a randomly selected class (or school).All school students of randomly selected classes were involved in the national research.4479 eighth grade students from 160 schools (212 classes) participated in the research.

Results
EFA was carried out in six steps of factor analysis: reliable measurements, correlation matrix, factor analysis versus principal component analysis, the number of factors to be retained, factor rotation, and use and interpretation of the results.In the application of factor analysis, it was taken into account that variables can be measured at a range level, normally distributed (Field, 2000, p. 444).The skewness (from -1 to +1) and kurtosis (from -1 to +1) of variable from questions group L1 were well within a tolerable range for assuming a normal distribution.Factorability was examined by measures of sampling adequacy.The Kaiser-Meyer-Olkin test (KMO-test) was used for sampling adequacy (KMO-test).The sample is adequate if the value of KMO is greater than 0.5.It was disclosed that KMO = 0.817 for the observed variables of questions in group L1.
All elements on the diagonal (MSA -Measure of Sampling Adequacy) of anti-image correlation matrix should be greater than 0.5 if the sample is adequate (Field, 2000, p. 446).All variables are suitable for factor analysis (Table 2).After having obtained the correlation matrix, it was decided to use principal component analysis (PCA) for investigating the variables of questions in group L1.The rule of Guttman-Kaiser was used for determining the number of factors.Initial eigenvalues indicated that the first two factors explained 46 % and 19 % of the variance respectively (Table 3).They explain 75 % of the variance.The third and all following factors explain smaller and smaller portions of the variance.Two factors (Table 3) correspond to Guttman-Kaiser rule.It means that two factors are appropriate for the data.The rotation method Varimax was used for the simplification of factor interpretation in PCA.After the Varimax rotation, the first factor explained the variance decrease to 33 %, the second factor explained part of the increase to nearly 33 % (Rotation Sums of Squared Loadings) (Table 3).
The last step in EFA was the interpretation of the results.The factor loadings are represented in the rotated component matrix (Table 4).The relationship of each variable to the underlying factor is expressed by factor loading.The variable You like Lithuanian language lessons has a correlation of 0,816 with Factor 1.Other three variables, You are interested in writing assignments in Lithuanian language lessons; You are gifted for the Lithuanian language; You are interested in reading texts in Lithuanian lessons, are also associated with Factor 1.Based on the variables loading highly onto Factor 1, we called it intrinsic motivation: interest, engagement, satisfaction.
The variables You are learning the Lithuanian language because you need to get a well-paid job; You are learning the Lithuanian language because it is important to obtain an interesting job; You are learning the Lithuanian language because it is important to obtain entry to a higher school; Thevb Lithuanian language is important for learning other subjects have high factor loadings on another factor, i.e.Factor 2. They seem to indicate the identified regulation: personal relevance, and conscious evaluation.Factor 2 was named extrinsic motivation: identified regulation: personal relevance, and conscious evaluation.

Discussion
The data of factor analysis of the questions in group L1 revealed two levels of motivation for learning the Lithuanian language: extrinsic motivation and intrinsic motivation.The first factor was named intrinsic motivation: interest, engagement, satisfaction.The second one was referred to as extrinsic motivation: identified regulation (personal relevance, conscious evaluation).
The questions You like Lithuanian language lessons; You are interested in writing assignments in Lithuanian language lessons; You are gifted for the Lithuanian language; You are interesting in reading texts in Lithuanian lessons are related with the factor of intrinsic motivation.Loadings close to -1 or 1 indicate that the factor strongly affects the variable.It means that the factor has a strong effect on the variable.Stevens (1992;in Field, 2000, p. 441) then "recommends interpreting only factor loadings with an absolute value greater than 0.4 (which explain around 16 % of variance)".This is only possible in principal component analysis.In our case, the principal component analysis was used and the value of all factor loadings was greater than 0,741.Two variables have the greatest factor loading with the factor of intrinsic motivation.The factor loading of the variable You like Lithuanian language lessons was 0,816; the factor loading of the variable You are interested in writing assignments in the Lithuanian language -0,783.The variable You are interesting in reading texts in Lithuanian lessons has less factor loading -0,741.Consequently, writing assignments are more important for the promotion of intrinsic motivation for learning the Lithuanian language by school students.
The statements You are learning the Lithuanian language because you need to get a well-paid job; You are learning the Lithuanian language because it is important to obtain an interesting job; You are learning the Lithuanian language because it is important to obtain entry to a higher school; the Lithuanian language is important for learning other subjects are related with Factor 2, i.e. extrinsic motivation: the identified level."A more autonomous, or self-determined, form of extrinsic motivation is regulation through identification.Here, the person has identified with the personal importance of a behavior and has thus accepted its regulation as his or her own" (Rayan & Deci, 2000, p. 62).Locus of causality perceived at the identification level of extrinsic motivation is named "somewhat internal".There are two locus of causality in our research: educational (You are learning the Lithuanian language because it is important to obtain entry to a higher school; the Lithuanian language is important for learning other subjects) and social (You are learning the Lithuanian language because you need to get a well-paid job; You are learning the Lithuanian language because it is important to obtain an interesting job).The variables of social identification have the greatest factor loading with the factor of extrinsic motivation: You are learning the Lithuanian language because you need to get a well-paid job -0.885;You are learning the Lithuanian language because it is important to obtain an interesting job -0.839.The variables of educational identification have less factor loading with the factor of extrinsic motivation: You are learning the Lithuanian language because it is important to obtain entry to a higher school -0.759; the Lithuanian language is important for learning other subjects -0.648.

Conclusions
Motivation for learning the Lithuanian language can be described by different variables: You like the Lithuanian language; You are gifted for the Lithuanian language; You are interesting in reading texts at Lithuanian lessons; You are interested in writing assignments in Lithuanian language lessons; the Lithuanian language is important for learning other subjects; You are learning the Lithuanian language because it is important to obtain entry to a higher school; You are learning the Lithuanian language because it is important to obtain an interesting job; You are learning the Lithuanian language because you need to get a well-paid job.Exploratory factor analysis allowed distinguishing two factors of these variables: the factor of intrinsic motivation and the factor of extrinsic motivation identified regulation: personal relevance, and conscious evaluation.
Extrinsic motivation for learning the Lithuanian language at the identification level involves a conscious acceptance of the personally valued benefit.The analysis of the benefit for learning the Lithuanian language revealed an educational (the Lithuanian language is important for learning other subjects; You are learning the Lithuanian language because it is important to obtain entry to a higher school) and a social (You are learning the Lithuanian language because it is important to obtain an interesting job; You are learning the Lithuanian language because they need to get a well-paid job) dimension.The educational benefit of learning the Lithuanian language for students is more important than social benefit.The data of Freedman test (χ² (3) = 193.439,p < .05)confirm a statistically significant difference between the students' answers to different questions about the educational and social benefit for learning the Lithuanian language.
Intrinsic motivation for learning the Lithuanian language is characterized by the self-determined behavior with a different background: an emotional (You like Lithuanian language lessons), a self-confident (You are gifted for the Lithuanian language) and an emerging personal interest toward the Lithuanian language (You are interested in reading texts in Lithuanian lessons; You are interested in writing assignments in Lithuanian language lessons).

Table 1
Descriptive statistics for the motivation of learning the Lithuanian language of 8th grade students(N = 4479)

Table 3
Initial eigenvalues of factors and rotation sums of squared loadings of questions in group L1

Table 4
(Ryan & Deci, 2002)atrix of the observed motivation for learning the Lithuanian language variables and the levels of motivation(Ryan & Deci, 2002)