Definición de las estructuras suspendidas

To investigate the bi-directional inter-relationship, as stated in section 4.7, between AIRCABS, and credit risk and liquidity crunch canonical correlation analysis is used in null hypothesis. In the first and second hypotheses to predict and explain the relationship between dependent variable and independent variables multinomial logistic regression is used. Furthermore, survey questionnaires analysed using Cronbach alpha, Kuder-Richardson, coefficient of variation and factor analysis.

4.9.1. Canonical correlation

According to Hair et al (1998), canonical correlation is considered to be the general model on which many other multivariate techniques are based because it can use both metric and non- metric data for either the dependent or independent variables. Multiple regression predicts a single dependent variable from a set of multiple independent variables, whereas, canonical correlation simultaneously predicts multiple dependent variables from multiple independent variables. Although other techniques impose more rigid restriction on the types of data with which they operate, Canonical correlation places the fewest restrictions. Canonical correlation considered by many researchers as a final effort to be used because other higher-level techniques have been exhausted. It has gained acceptance in many fields and represents a useful tool for multivariate analysis. Canonical correlation analysis is a multivariate statistical model that facilitates the study of interrelationships among sets of multiple dependent variables and multiple independent variables (Green & Carroll, 1978 and Green, 1978).

The canonical correlation analysis develops a canonical function which maximises the canonical correlation coefficient between the two canonical variants. Canonical correlation coefficient measures the strength of relationship between the two canonical variants. Canonical correlation analysis is a useful and powerful technique for exploring the relation‐ships among multiple dependent and multiple independent variables (Hair, Black, Babin & Anderson, 2010). Canonical correlation analysis reveals how the two sets of independent and dependent variables strongly related, their strengths of the relationships, and their nature of the relationships defined.

The following specifically set out the advantages of using canonical correlation analysis.

 It limits the probability of committing type one errors which is related to the likelihood of finding statistical tests. While using multiple regression a separate statistically significant tests for each equation, for one independent variable to many dependent variable, substantially increases the risk of type I error. Canonical correlation can access these relationship between the two set of independent and dependent variables in single relationship rather than individual variable (Fan,1997 and Thompson, 1991).

 Canonical correlation is able to analyse data involving multiple dependent and multiple independent variables and it is theoretically reliable with that purpose.

 It shows the strength of correlation between two sets of canonical variates

 It helps to determine sets of dependent and independent variables are independent of one other and the magnitude of the relationship that existed between the two sets.  The linear combination of sets of dependent and independent variables are maximally correlated since canonical correlation derives a set of weights for each set of dependent and independent variables. (Hair et al, 2010).

Since canonical correlation concerns to reveal the strength of the two set of independent and dependent variables, analysing the relationship between credit risk and liquidity crunch on one hand and AIRCABS on other hand using canonical correlation would help us to show the basic relationship.

4.9.1.1. Canonical Correlation Analysis

Canonical correlation is a multivariate technique that helps to identify the nature, magnitude and relationships within a set of dependent/independent variables and across two sets of independent and dependent variables. The dependent variable for the research under study is AIRCABS and the independent variables are credit risk and liquidity crunch. Since the observation per independent variable is 60 according to the guideline, the sample size is sufficient for canonical correlation and Type II error will not be a problem when the null hypothesis does not reject it when it is false (Henry, 1990; Harrell, 2001). The independent and dependent variables in canonical correlation analysis are detailed in table 4.l

Table 4.1: Dependent and independent variables used in canonical correlation analysis Independent

Variables Indicators Measurement level

Variable nature in bi-directional

correlation Liquidity Crunch Deposit Run (D/TD) Continuous (Time) Independent

/dependent Variable Credit Crunch (L/TL) Continuous (Time) Independent

/dependent Variable Liquidity Risk (LA/TD) Continuous (Time) Independent

/dependent Variable Credit risk Non-performing Continuous (Time) Independent

Independent Variables Indicators Measurement level Variable nature in bi-directional correlation asset ratio (TNPLs/TL)

Credit risk (LLp/TL) Continuous (Time) Independent

/dependent Variable Commodity price shock

(P/P)

Continuous (Time) Independent

/dependent Variable Dependent

Variable

AIRCABS Non-interest income

(NIN) Growth rate income Total NIN r 

Continuous (Time) Independent

/dependent Variable

Bank’s Efficiency ratio

(EFR) Continuous (Time) Independent /dependent Variable Return on asset (ROA) Continuous (Time) Independent

/dependent Variable Return on equity (ROE) Continuous (Time) Independent

/dependent Variable Capital adequacy ratio

(CA)

Continuous (Time) Independent

/dependent Variable Source: Author

The variables’ indicators in figure 4.3 are canonical variable of AIRCABS, credit risk and liquidity crunch, the interrelationship of which can be canonical correlation. The relationship between independent and dependent variable indicators employed in canonical correlation is depicted in figure 4.3.

Figure 4.3: Canonical correlation between canonical variants of AIRCABS, and credit risk and liquidity crunch

Source: Author

Since canonical correlation reveals the strength of two sets of independent and dependent variables, analysing the impact of credit risk and liquidity crunch on AIRCABS using canonical correlation shows the basic relationship. Canonical correlation analysis solutions are sensitive to changes of variables such that the change of variables in one variant can be noticed when changing the composition of other canonical variates. Suppose the credit risk and liquidity crunch components are represented by (x) and the AIRCABS components are represented by (y), as independent and dependent variables respectively. Since each credit risk and liquidity crunch, and AIRCABS component variables vary across and within the group, the equation of canonical correlation is calculated as:

1. Non-interest income growth rate (NIN) 2. Bank’s Efficiency ratio (EFR) 3. Return on asset (ROA) 4. Return on equity (ROE) 5. Capital adequacy ratio (CA) Liquidity Crunch AIRCABS Credit Risk 1. Deposit Run (D/TD) 2. Credit Crunch (L/TL) 3. Liquidity Risk (LA/TD) 4. Non-performing asset ratio (Total NPLs/Total Loan) 5. Credit risk (Loan loss provision/Total Loan) 6. Commodity price shock (P/P0 )



Credit risk and liquidity crunch (x) = AIRCABS (y) which can be expressed by weights cannonical are B and ) ( crunch) Liquidity and ( t t    where AIRCABS B W risk credit A U t t

The correlations between the linear combinations are termed canonical correlations. In the maximisation process, there are pX and qY pairs of variables respectively, such that for which maximum p canonical correlations are generated. Consider for p vectors of U and W variates are sampled such that,S_xx and S_yy are within-set variance-covariance matrices and S_xy

is covariance matrix for the vector X and Y.

The linear combination of credit risk and liquidity crunch variables (U) with a group of set AIRCABS (w) by using each set of variables can construct credit risk and liquidity crunch, and AIRCABS variants through the following equation