 Konfirmative factor analysis differs from the exploratory factor analysis in that in a converter factor analysis a researcher specifies the factors for the data instead of having the computer discover what are the underlying factors. So converter factor analysis requires that you specify the expected result and then computer will tell you if that result fits your data and will estimate the factor loadings for you. This is a more flexible approach to factor analysis than an exploratory analysis. In this video I will demonstrate you on a conceptual level what converter factor analysis does and how it can be applied to more or different kind of scenarios. Our data has three or six indicators. We have indicators A1 through A3 that are supposed to measure construct A so we can see that there is variation in these indicators due to construct A and there is also some random noise at the E here so that's unreliability of these indicators and then we have some variance components that is reliable so for example if we measure A3 multiple times there is a specific part of the A3 that is reliable but it is specific to A3 so for example if we ask whether a company is innovative or not that measures innovativeness it can also measure something else so the only unreliability is not the only source of measurement there but there is also some item uniqueness and the idea of a converter factor analysis is that we specify a factor model for this data ourselves so for example we would say that because these are three indicators A1 through A3 are supposed to measure construct A we assign them to factor A and then we assign these to factor B and then its indicator also gets an error term then the factor analysis takes the variance of those indicators apart into variance that can be attributed to the factors and variance that can be attributed to the error terms like so so now we have a factor solution here we have all variation that is due to our construct A goes to factor A all variation that is due to construct B goes to factor B and all these are item uniqueness and unreliability goes to their terms that are assumed to be uncorrelated so these are uncorrelated distinct sources of variation for each indicator and then we have the two common factors so that's the idea of case sometimes your data are not as as great as you would like and a converter factor analysis allows you to model also problems in your measurement so for example if we have this kind of scenario there is a variation again due to construct A variation due to construct B and then we have unreliability the black circles here and we have unique aspects of each indicator but there is also some variation in A3 and B1 that correlates the variance component are here these these letters are no particular meaning by the way they're just letters to distinguish these different circles so A3 and B1 correlate for some other reason than than measuring A and measuring B that could possibly be correlated if we feed the converter factor analysis model then this variation that is shared by A1 A3 and B1 actually goes to the factors the reason why it goes to the factors is that these error terms are are constrained to be uncorrelated and what happens now is that our factors which are supposed to present construct A and construct B are contaminated by these are secondary source of variation are that are present in A3 and B1 and as a consequence the correlation between factors A and B will be overestimated and our results will be biased and this is also the case in exploratory factor analysis so if you have two factors that influence or if we have this kind of like minor factor that influences A3 and B1 and we only get two factors then the factor correlation between those two factors will be inflated if we were to run an exploratory analysis then the exploratory analysis could identify that there is a third factor that loads on our A3 and B1 but because it's just two indicators it's also possible that the exploratory analysis wouldn't identify that factor for us so what can we do with this kind of situation a converter analysis allows us to also model correlated error so instead of specifying that these error terms of A3 and B1 are uncorrelated we can say that it's possible that A3 and B1 correlate for some other reason so we relax the constraint we specify that these two can be correlated and then the the variation in A3 and B1 that is shared between these indicators but not with others so it's not part of the factors then gets to escape to these error terms and then we also again get clean estimate of the factor correlation A and B but this is something that many people do so your statistical software will tell you that the model doesn't fit the data perfectly and it'll also tell you that you could freeze some correlations to make the model fit better and but that's a bit dangerous unless you know what you're doing you should only add this kind of correlated errors if you have a good theoretical reason to do so so the fact that your statistical software tells you to do that you could do something to increase the model fit is not a reason to do something it's an indication that you could do something and you should consider something it's not a definite guideline that you should actually do that so under which scenario then are you are is it a good idea to allow the error terms of two indicators to correlate for example if our indicators are would look like that so we would have indicators about innovativeness so A here A factor here is innovativeness and B factor is productivity so we would have questions about innovativeness and questions about productivity then we realize that okay so A3 is our personal is innovative and B1 is our personal is productive so both of these actually have this this personal dimension as well so they don't measure only innovative and productivity they also measure how high quality the personnel in the company are so then we realize that okay so there is a secondary dimension that these two indicators measure and then we can add the error correlation here but it also you have to justify it so it's not enough that you say that our statistical software tells us that the model fits better if we do something you have to justify it also in non-statistical terms this is the same thing like with the outliers you don't delete an observation because it is different you have to explain why it's different in non-statistical terms the same thing when you are eliminate indicators from a scale so your statistical software will tell you that sometimes eliminating an item from a scale will make chromebacks alpha to go up but that's not the reason to eliminate an item you should also look at non-statistical criteria so what does the item look like is there a good reason why we think it's less reliable because these kind of are suggestions by your software they could also be just a random correlation between two random elements so random correlation between these is and then you would be mis-specifying the model another way perhaps a bit better way to accomplish the same is to specify this secondary factor so we could instead saying that these two error terms are correlated we could say that these indicators A3 and B1 actually also measure something else so we add this secondary factor here and this is a bit more appealing approach because then it makes you have to explicitly then interpret what this factor means and it's a lot easier to free correlations without explaining what they are actually what's the interpretation of these two of the correlation between these error terms it's a lot easier to do that without an explanation than adding a factor so if you had to add a factor then your reviewers will ask you to explain it and you always should so it's a good idea to have the factor instead of having the correlation mathematically both of these accomplish the exact same thing they allow the unique aspect of A3 and B1 that is correlated to escape from the error terms this example of adding the minor factor can be extended to also another scenario so that's just the same indicators again we can have this kind of scenario so what's the scenario here we have indicators A1 through A3 measure A indicators B1 to B3 measure B there's unreliability there is and then there is some variation that is shared by all the indicators that variation could be for example variation due to the measurement method so this is a scenario where you would have common method variance so the R would be here the variation due to the method or the common method variance and then we if we estimate a factor model with A1 A2 and A3 loading on A and this B indicates loading on B then all variation due to the method escapes to this B factor and A factor and the factor correlation will be overestimately greatly so in this kind of scenario it is possible to also specify a secondary factor so we can specify this method factor here and the idea is that all the indicators load on the factors they're supposed to measure the factors representing the constructs and a factor representing the measurement process so looks really good and looks too good to be true but this is not the panacea for method variance problems there are this kind of model is problematic to estimate the reason for that is that a high correlation between A and B is nearly indistinguisable from A1 A2 A3 B1 B2 B3 just being caused by one factor so they are empirically are nearly impossible to distinguish so this kind of model is very unstable to estimate in practice these models are have been shown to be problematic even in simulated data sets but there's one way that this kind of model can work and it's if you add these marker indicators so sometimes you see in the published papers that they use marker indicators the idea of marker indicators is that you have indicators that are unrelated with the factors that you are modeling so A1 and B1 B are unrelated to this M1 M2 for example if you use innovativeness and productivity and then you have questions on one to seven scale you could have a marker indicator of whether the person likes jazz music or not i've actually seen that being used the idea is that how much you like jazz music is completely unrelated with the innovativeness and productivity of your company but if the jazz music indicator correlates with these indicators then we can assume that that correlation is purely due to the measurement method because jazz music liking and innovation really are two are completely different things