 � tier is the factor analysis model. a factor analysis basically Americans model based technique principle component model based technique jamie bothcond jimmy modell avo model America basically how sepeose we have the observation of pーー a variables Seho we have the Pーー a variables which have mean Zucker Andýun school uhh chains madriga Se겤aha anyer and Обst IT in explaining the corełamta i1,f1,factor 1, lamda i2,factor 2,upto so on lamda i k,factor k, plus epsilon i error i e i. Where, i varies 1 to p. So, we have the p variables and kind of we have here factors 1,f1,f2,upto so on fk, total k factors 1,plus error. On,in the matrix notation, अब इस्सी मोडल को अब हम मेट्रिक्स नूटेशन में लेक्रें एक्स पी क्रोस वान ये एक्स आप आप आप आप आप योट्योंध के लिए, this is the matrix form आप के पास कितने है, p rows and one column x, and here is the capital lambda ये आप के पास स्मोल लेंबात है, अब हम दे असको मेट्रिक्स वान में हमारे पास मुल्तिप्लायब बाए आप आप एक्स थन्ट फर्ट्तर, और कितने फक्तर से हमारे पास है, k into one, k rows and one column का हमारे पास फक्तर होगा, प्लास आबडर, आबडर कितने है, p cross one, p rows and one column, तो this is the notation of the model, model कि नूतेचन किस में mattress is formed में अब आप को पता है, हर model के कोईना कोई अजम्छन्स होती है उन अजम्छन्स कोम चेख करते हैं where f, f stand for factor, and e is the error, that is 5 the expected value of f which is equals to 0 the first condition, first assumption and the covariance of the factor which is equals to identity यह यह यादो नहीं अई हमें further, we can do our mathematical derivation only if we have this idea and this is our idea because we have seen that basically what we have has the mean, mu and variance covariance so according to the properties of the normal expected value of the f which is equals to 0 and the covariance of x which is equals to identity and next expected value of error you know that you have seen in regression also, you have seen in argument expected value of error which is equals to 0 and covariance of error which is equals to psi this is the sign of the psi vector psi now basically vector psi which is equals to the diagonal of the variance of e so psi हमारे पाज क्या है diagonal values किसकी? variance of e which e हमारे पाज क्या है this is the e error whose variance हमारे पाज क्यो diagonal variance है that is called the psi and which is equal to covariance of e here is the assumption of the factor analysis model the factor analysis कि हमारे पास अजम्शन क्या है क्योंके इस में आजम्शन से बहुत है factor analysis कि उसके अकोडिंग हम देख रहे हैं the factor analysis model assumes that there are K underline factors you know that we have K factors जो हम बनाएंगे अस में where K is less than equals to P जाहरे आपके पास जो नमबर अप वेरिबल हैं उसके लेस होगा के यान क्या आपके पास क्या है total number of factors total number of factors which is less than the number of variables which is denoted by F1, F2 upto so on FK so we have the K factors and each observed variable is a linear function of these factors together with our residual variate अभी हम नहीं किया इं सारे factors के साथ it's a linear function of these factors together with the residual variate so that aayat variable can be written as this previous अभी हम नहीं यही model में देख है उसको हम ने लिकने का मेड़ है this is the equation number one equation number one अभ ये लेम्दास क्या हैं इस लेम्दास कोम कैते हैं in the above equation the weights this is the weights this is the weights are usually called the factor loadings अभ ये जो वेट से हैं इसको हम factor analysis में इस लंगवेच में हम क्या कैते हैं factor loadings so factor loadings ये जो लेम्दास हैं these are the factor loadings so that लेम्दास क्या है is loading of aayat variable this is the लेम्दास क्या है is the aayat variable on the kya factor ये aayat variable of the kya factor the variates ये aayat describe the residual variation and this is called the specific factor अभ हमारे पस क्या है 2 parts हैं 2 parts में मारे पस क्या है लेम्दास are the factor loading and aayat are the specific factor ये हमने याद रखना है this is the equation number 1 so we have the sum another assumptions that is the specific factor क्या ता specific factor हमारे पस ये aayat are assumed to be independent of one another of the common factor f simple जो मारे पस normal के अजाम्चन ती तेम उसी तर हमारे पस यापे अजाम्चन से in terms of aayat the specific factor ये aayat are assumed to be independent of one another of the common factor f k the second assumption the common factors किसको हम ने का है the common factor बेसेकली हमारे पस f 1, f 2 these are the common factors and common factors are independent of one another the second assumption हमारे पस the factors वो एक तुस्रे से the factors वो the factors वो एक तुस्रे से the third we have assumed that x i have zero mean and it is assumed that all factor have mean zero this is the third assumption and the fourth it is usually to choose the common factor so that each has unit variance किसकी अजाम्शन है the common factor that has each unit variance but the variances of the specific factors may vary with the variance of the e i specific factors वो वेरी करेंगे अपके पास so हम ने उसके नोटेशन क्या रख है variance of e i that is called the style it is usually to assume that the common factor and the specific factor both have the distributed with multivariate normal distribution this implies that x x vector is also have the multivariate normal distribution को फोलो करेगा these are the basic assumptions where x transpose x अपके पास है vector which is equals to x1, x2 up to so on xp the large number of assumptions to be made in set up the factor analysis model is one of the drawbacks of the method अब हमारे पास हर मेथर की कोई ना कोई drawbacks भी होती है factor analysis के basically drawbacks क्या है के इस में large number of assumptions होती है लेकिन ये सरवेस में psychology में sociology में market service में सब से जाता important factor जोता होता सब से जाता important analysis जोता is factor analysis होता तो हम इसको further अब आगे देखते है के factor analysis अपलाई कैसे होगा