Methodology and Model Specification

When applying factor analysis to relevant research, there are usually two types of methodologies adopted by researchers. The first type of factor analysis is called the Exploratory Factor Analysis (EFA). This methodology is mostly used on collected

variables which does not have any existed factors fitting the observed data.16 _The

second factor analysis is called the Confirmatory Factor Analysis (CFA). In CFA, researchers attempt to test the hypothetical factor model with statistically signifi- cant results, which means using the existing variables to confirm the model. One of the advantages from the CFA is to show a methodological refinement on revising the measurement error issue. In regular regression or other path analysis, the observed variables are not always perfect on measuring all phenomenon, and sometimes re- searchers just assume those observed factors are perfectly valid and reliable. Most of the scholars do not correct the measurement error issue, which will easily cause

problems on biased parameter estimates (Kim and Mueller 1978a;b; Schumacker and

Lomax 2004). Thus, adopting CFA can help researchers to general some latent vari- ables, which will take account for the measurement error of variables.

The functions are different between EFA and CFA. In EFA, we mainly ask how many underlying dimensions there are for the given data, and we can quickly ascertain the minimum number of hypothetical factors that can account for the data. In short, EFA is used for data reduction and dimensional exploration. It is also applicable to generate one latent variable representing the whole concept of abstract variable. For example, EFA can help us generate the overall value for the ideas of national interests from the collected policy variables.

However, in order to have a more comprehensive explanation and investigate the theoretical dimensions of policy interests, it is important to consider a more heuris- tic device which can examine the hypothetical factors with directed path structure. Based on previous theories, we can assume that there are three focal dimensions for states’ policy concerns, including security, economic, and community. CFA can

16_{Scholars explore which observed variables define each construct or factor (Kim and Mueller}

1978b). In exploratory factor model, we seek to find a model that fits the data and has a theoretical support for it. Besides, in EFA, the researchers explores how many factors there are, and which observed variable explain the factors more than others.

help us to see if there are any model misspecification in the hypothetical model. For instance, some issues related to whether we should put state development into com- munity or economic concerns. Here, CFA may be used as a mean of identifying the more appropriate model by comparing the model fit indices. The statistical outcomes offer a strong function telling us whether we should put development into community or economic concerns for this project. In general, CFA offers better understanding about the real meaning and dimensions for the key variables.

The mathematical functions for the factor analysis in this project are shown below. These functions of linear combinations are derived from the path diagram in Figure 2.1 which implies the assumptions of total latent factors representing the observed policy variables. We can summarize the nine equations to a more general form of equation relating to these nine indicators in equation 2.2.1.

X1 = b11f1+b12f2+b13f3+U1 X2 = b21f1+b22f2+b23f3+U2 .. . X9 = b91f1+b92f2+b93f3+U9 Xi =BijFj +µi (2.2.1)

From the equation 2.2.1, there are i policy indicators where i=1,2,. . . ,9. The total latent variables (or factors) are represented in j (j=1,2,3). I assume that the random

error, µi, should be uncorrelated with Fj and that E(µi) should be zero.

The model I apply cannot be estimated by traditional factor analysis proce- dure. I follow the recommendation from previous research by running LISREL model (Jöreskog and Sörbom 2001). Jöreskog and Sörbom’s LISREL 8.8 offers the analysis

of covariance structures to help estimate policy interests. The model I assume is that more concrete policy interests are determined by more abstract concerns at the higher level. The first order CFA provides the identifications for the relationships be- tween abstract concerns and specific policy behavior. For example, security concerns have more influence on alliance, national capability, and nuclear weapons possessions. Economic concerns will lead to more activities on trade, foreign direct investment, and market openness. Community concerns will help states to think more about their general quality in the international society, which will be imperceptibly influenced by their policy preferences on revising their regime types, joining certain international organizations, or developing domestic living standard. The first level of CFA thus introduces a clear picture identifying the diversified states’ behavior with clustered national objectives.

The second level of order reveals that each concern is assumed to be determined by the core value of national interests. Since it is extremely difficult to list out all policy concerns for each state, this approach offers an efficient and parsimonious analytical framework. I argue that national policy concerns can be categorized by three main groups, and each has direct link to the core value of national interests (This structure composes the second order of the CFA model). In short, a hierarchical ordering shows that a more abstract idea can be explained by a slightly clear concept on the next order (Figure 2.1).