 Student, this is the very important topic in multivariate analysis that is the factor analysis. What is the factor analysis? We study in this, what is the factor analysis basically? The factor analysis abbreviated to as a FA, FA stands for factor analysis is a variable drive technique that is appropriate when the variable arises on equal footing. Now equal footing, we will see what is the idea of equal footing here. The idea is to drive the new variable called factor. Now how did this factor come about? We have the series of variable, now series of variable for psychology, I will give you an example, I mean feeling sad, I don't feel like working, lack of interest in daily activities and lack of self-confidence, I am not able to sleep, I mean anxiety factors are happening, now I am feeling anxiety, all these things, I feel that if I keep the name of this group depression, in which feeling is also sad, I don't feel like working and I am not in mood. So this type of variable that you have, we have made it a factor that is called the depression. Now the series of variable that you have will reduce in one factor, and that factor is called depression. Now I will study all the variables, I will study that factor. Now what is the equal footing, that all the variables that you have are coming, no variable we will not eliminate from here, but we will see that this variable which is brought into the group, we will make that factor, means we will make that group, we are saying that group, this is the factor. The variable arises of equal footing, the idea is to drive the new variable called factor, of new variable, that is how the factor was made, you have the same variables which we were studying, we saw that this is going into the factor, this is going into the case group, we gave them the name factor, which will give us better understanding of the data. Now instead of doing all that, we are studying the factor of depression. Factor analysis is a statistical technique used to identify pattern in a set of data and to determine which variable are most closely related to each other. It became clear that how we made a group of variables like one, which you have related variables, closely related to each other, which we called observed variables. The goal of the factor analysis is to reduce a large number of variable into a small number of factors, or latent variable that can explain the pattern of the observed in the data. What did we do? We have reduced a large number of variables into a small number of factors. Now in the same way we have next, they can explain the pattern of the observed variable, the observed variable feeling sad, lack of interest in daily routine, lack of self-confidence. What did you have? We made the observed variable factor. Factor analysis is based on the proper statistical model, yes, principal component, proper statistical model was not there, but factor analysis we have a proper statistical model. That is more concerned with explaining the covariance structure of variables, then with explaining the variance structure. Principal components we check variance structure, and factor analysis we study with variance structure. Factor analysis is a statistical method that is used to identify pattern in data and reduce the dimensionality. Now how will we reduce dimensionality, because the variance you have, the variables are converted into factor by finding underlined latent variables or factor. It is commonly used in the social science, yes, we can use it in social science, you have psychological factors, we use it in medical science, that what you have, you are telling the disease, you are telling the symptoms, you have these symptoms, cholesterol high or BP or sugar patient, we have all these symptoms, we are following this disease. So, the variables we have, the symptoms basically are the variables, we have told those variables that if these symptoms are there, then what disease are we following, blood sugar is going in a group, we are following that. So, you have it is commonly used in the social science, psychology, marketing, health science here, health may be used a lot factor analysis and other field to uncover relationship between the different variables and simplify complex data structure. You have so many variables, complex data, you have it, we have converted it into different factors. In other words, factor analysis help to simplify complex data set by identifying factor that contribute the variable observed in the data. Okay, one more thing is that you have the same kind of variable, you are converting it into factor, but we have to do this very carefully, for that we have the software, we determine the SPSS from there, but before that, we have to check all its assumptions. For example, if you have a survey with a large number of question, factor analysis can use to identify the key underlying factors or themes that are being measured by the question. Same key point, we have discussed that we have large number of questions, large number of questions means we have variables. Now, how do we handle that large number of questions? We have converted it into different groups, now we will study the factor. Now, we can study it along with another factor, we will study it along with factors. The goal of factor analysis is to explain the correlation structure. Now, the correlation structure is that we can study that group along with another group. Among a set of observed variable in terms of a smaller number of underlying or latent factors. The factors are not directly observed, but from the observed variable. Factor analysis assume that the observed variable are influenced by the underlying factor which are mired with error. Now, we have an assumption that we will check it this way. So, there are two main types of factor analysis. First, we have explanatory factor analysis and other is the confirmatory factor analysis. Explanatory factor analysis. Now, what I have explained to you is explanatory factor analysis. It is to use to identify the underlying factor that best explain the correlation structure among the observed variable. Now, we have done all this, we will check the correlation structure in factor analysis. CFA. CFA means confirmatory factor analysis is used to test whether a pre-specified factor model fit the data well. Now, before the confirmatory analysis, we need to know how the factor analysis should be. So, your basic sleigh bus is basically explanatory factor analysis. After that, we can also study the confirmatory factor analysis. Now, how to do factor analysis on HPSS? How can we find it? You have some steps. The step for conducting factor analysis are as follows. Decide on the number of factor to extract. How will we decide? We can decide using the eigenvalue or the screen plot. The basic is how to extract the factor according to the eigenvalue. Where does the eigenvalue come from? It comes from the principal component analysis. So, we have the principal component analysis that we are finding here. And here we are checking the screen plot. And the parallel analysis. The second step is choose the method of factor extraction. Now, how to choose factor extraction? There are several methods including PCA, principal axis rotation, maximum likelihood and others. We have the options in HPSS that we have to extract the factor according to the principal component. We have to extract the principal x factor according to MLE. Now, the third step is to determine the rotation method. We can easily determine the factors from the rotation method. We have rotation methods with very max and orthogonal rotations. And the fourth, evaluate the model fit. This can be done using a variety of myers such as the chi-square test. The model fit is when you have one factor determined. We have to do one factor testing. What can we do for that testing? We have the factor that we have made. We have a code or an error in it. To check that, we are testing that factor further. We can also use the chi-square test. We can also test the comparative fit index according to the root mean square error. That is, we will test the factor that we have made. Finally, we have to interpret the results. Look at the factor loadings. What are factor loadings? Basically, according to these factor loadings, we make factors. Look at the factor loadings. We have to determine which variable is more strongly related to each factor. According to those factor loadings, we determine which variable is strongly related to other factors. Factor loadings represent the correlation between each variable and each factor. So, factor loadings, this is another important thing in factor analysis. What are we checking through factor loadings? Which variable is strongly related to that factor? Factor loading represents the correlation between each variable and each factor. Further, after checking the factor analysis, we will read it in detail on software. So, this is the basic idea of the factor analysis.