 Suomessa, kun otamme varmasti varmasti varmasti tai varmasti varmasti varmasti, olemme ajattelut, että nämä varmasti ovat unidimennettäisyydellisiä yhdessä tai yhdessä konseptille, ja se, että otamme varmasti, on se, että otetaan enemmän kompositiivinen varmasti kuin kaikille ihmisiä, jotka ovat kompositiivisia. On myös yksi asia, että otamme varmasti tai varmasti varmasti tai varmasti varmasti ja se on kuitenkin indeksikonstruksia. Kwhen and why, which you want to use indesses instead of raw variables, is the topic of this video. To understand indices, we have to first understand what is a scale variable, what is a non-scale variable. I refer to as a scale variable, a variable that is part of a measurement scale. For example, these three questions here form a survey scale that is supposed to measure company's innovativeness. Tämä on unidimensiona-kaaleja, tai ainakin se on se, että se on unidimensiona-kaaleja. Tämä tarkoittaa, että asioita on the same quantity, ja asioita ovat hieman korreettisia. Joten asioita on hieman ympäristöryhmässä, jotta asioita on hieman ympäristöryhmässä. Ja hieman ympäristöryhmässä, jotta asioita on hieman ympäristöryhmässä, jos asioita on hieman ympäristöryhmässä, niin normaalista asioita, jotka asioita on hieman korreettisia, ovat ympäristöryhmässä. Innan jälkeen, kuten asioita on hieman korreettisia, kuten asioita on hieman korreettisia, vaan kun on hieman korreettisia. Tämä voi olla tietysti ympäristöryhmässä, jotta käyttää enemmän asioita ja asioita on hieman korreettisia. Täällä on tietysti asioita, jotka asioita, jotka eivät ole nämä asioita. Joten asioitamme non-scale asioita, jotta kaikki asioita, jotka eivät ole non-scale asioita, ovat non-scale asioita. Asioita voivat olla asioita ympäristöryhmässä, jotta esimerkiksi asioita on hieman tai hieman ja asioita voivat olla korreettisia tai ne voivat olla korreettisia. Tytäkinä asioita, jotka eivät ole käyttäneet non-scale asioita, jotka voivat olla asioita, ovat alkoholkonsumption. Alkoholkonsumption on tärkeää asioita, asioita ja hieman ja asioita, jotka voivat olla. Tämä 3 kategorit ovat ehkä ei ole hyvin kokeillaan, koska esim. ihmisiä voivat olla asioita tai hieman ja ihmisiä voivat olla asioita tai hieman ja en ole paljon ihmisiä voivat olla asioita. Tämä on yksi kategorit, jossa on tärkeää asioita, jotka voivat olla asioita. Toinen asio on, että asioita, jotka voivat olla asioita, ovat eri kokeillaan kokeillaan, jotka ovat the same behavior. Jos ihmisiä voivat olla asioita tai hieman ja asioita, niin se voi olla tehnyt muutamaa kaikenlaisia. Jos esimerkiksi, jos hieman asio on tehnyt, että kaikenlaisia on 15 eri asioita, että hieman asioita voivat olla asioita tai hieman asioita, niin hieman asioita voivat olla asioita tai hieman asioita tai asioita. Tämä on yksi kategorit, joka voivat olla eri asioita tai hieman asioita. Joten miten asioita voivat olla asioita? Ja kun olet useita asioita? Voodoo economic book on hyvä esimerkiksi, kun olet useita asioita. Seuraavaksi, hän useita asioita ja eri asioita kategorit. The expenditure categories, how the schools spends their money are correlated because schools that have more money spend more and then schools that are poor don't spend as much. If we have let's say 20 different ways that schools can spend money and then we have let's say 100 schools running a rigorous analysis would be a bit problematic because of multicollinarity. The idea would be that because we have so many categories we can't really say whether any of them matters independently. What if we are interested in the more general question does the school expenditure, how much money you spend overall and not whether it's in a specific category, how does that influence student performance? Then we could take a sum of all the spending categories and then use that as an explanatory variable in a rigorous analysis with the student performance as the dependent variable. That would make a lot of sense unless we are specifically interested in a particular category and how much that contributes. So when our research interest is in this higher level concept like spending instead of spending in a particular category and when we have a small sample size then taking an index would be a reasonable thing to do. Of course if we had a million schools in our sample it's unrealistic but if we have that then modeling each of these expenditure categories as separate explanatory variables in the rigorous analysis would be possible and that would be the ideal thing to do. When we do indices there are a couple of statistical assumptions that we make and then we have to decide whether those assumptions are reasonable. So let's consider that we have an index C defined as a sum of x1, x2 and x3. For simplicity I'm just using a sum I could also be using a weighted sum. The index can be used as an independent variable or as a dependent variable in the rigorous analysis. If we use the independent, the rigorous, the index as an independent variable that is the same as assuming that all of these variables x1, x2 and x3 here in the rigorous model have the same effect beta 1 on the dependent variable. Does it make sense to assume that they are the same? The model probably is not strictly correct but if we are interested in just understanding the overall level of spending of a school then taking the sum of different spending categories would be okay. If we are interested in understanding the effects on persons height and weight on for example how much the person exercises then assuming that those two height and weight have the same effect would be unreasonable because that's so unrealistic and we normally want to know the different effects of height and weight. So what if we have the index as a dependent variable? The scenario is very similar. In this case having an index as a dependent variable is the same as having a separate rigorous model for each component that goes to the index. And we assume that the independent variable z here has the same effect beta 1 on each part of the index components. For example if we are modeling how much the change in the principle of a school influences the spending then running that kind of model would be reasonable if we are only interested in the overall level of spending and not specifically on any spending categories. Trying to understand how whether exercise influences that sum of your height and weight would be unreasonable because you can't change your height by exercising but you can influence your weight. So whether it makes sense to use indices can be also thought through this approach. Does it make sense to assume or approximate all these effects to be the same as effect or as causes of the index? So a summary of how do you do indices and when would you like to make one? The idea of indices is that the construction index doesn't validate anything. So you can take sums of things that are unrelated, sums of things that are invalid or unreliable. Just the act of taking a sum does not provide you any reliability or validity evidence. Therefore if you take variables and do a sum you have to validate and assess the reliability separately before you start forming the index. If we are doing, for example, a stock indices then we know that the stock values, individual stock values are valid and reliable by definition because the numbers are what they are. If we have survey measures we ask people how much wine they drink, how much beer they drink, how much hard liquor they drink, then we have to validate and assess the reliability of those survey measures before we form an index. Then we have to justify the index and does it make sense to sum these three different variables. I can think of two different justifications. One is that the variables that go into the index present different quantities or different forms of the same thing. So wine, beer, hard liquor all present different forms of alcohol. Or they present different ways that the behavior can manifest. For example are different ways that you can redesign your supply chain. The third thing that you have to do is to justify why are using an index over separate items. And this has to do with the level of theorizing. So are you interested in a higher level question of, for example, does supply chain redesign matter at all? Or are you interested in understanding what kind of supply chain redesign matters? Are you interested in whether alcohol drinking or beer drinking versus wine drinking causes health problems and so on. The justification can also rely on sample size. So if you have a small sample then that sets limitations on what we can do. If the sample is very small then estimating these different effects of different index components is going to be so imprecise that it doesn't make sense. So in small samples indices are probably more useful than the separate row variables. But that must be justified in your research report. Then the final thing is that are how do you set the weights? The index weight should not be defined empirically because there is no good way of doing so without causing problems. So you set the weights based on theory. For example are if you have no idea of how much those different indicators should contribute to the index. You don't know whether one indicator is more important than another one. Use equal weights. And that's typically, that's probably the best recommendation in any case. Finally if you do indices which often is a reasonable thing to do just to get your study published it may be a good idea to avoid the term formative or formative measurement or causal indicator in your study because otherwise reviewers will challenge you to defend that your indicators cause the construct and that's the key problem. That's an unrealistic thing in the formative measurement literature. So to summarize taking indices of different variables is okay but saying that the indices cause the construct that is the problematic idea.