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Aggr, Ego Fallacy, Simp Para, ICC, Design Effect - Coggle Diagram
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Aggr, Ego Fallacy, Simp Para, ICC, Design Effect
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Simpson‘s Paradox – Nichtberücksichtigung von Gruppen (Level-2) kann zu völlig anderen Resultaten führen.
- Beispiel – Arbeitszufriedenheit
- Verantwortung (Prädiktorvariable) und Arbeitszufriedenheit (Zielvariable)
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- Zusammenhang zwischen Verantwortung und Arbeitszufriedenheit
- ⇒ neg korrel ⇔ Je höher die Verantwortung, desto tiefer die Arbeitszufriedenheit.
- ⇒ Simpson's Paradox
- Simpson‘s Paradox – Nichtberücksichtigung von Gruppen (Level-2) kann zu völlig anderen Resultaten führen.
- "if you dont consider the upper grp levels, you get a diff correl line than if you do consider the grps"
- eg tog Streuung looks like a neg correl, but considering the grps you get a pos correl per grp - and the MLM will show the avg of the pos correls per grp
why?:
- Die drei Firmen unterscheiden sich deutlich bzgl. der durchschnittlichen Verantwortung. (Verantw levels are diff btw the Firmen)
- wie auch der mittleren Arbeitszufriedenheit! (the Firmen means)
- again nicht Unabh, bc those in the same Firma have Abh!
- so u gotta make them Unabh then..
- by separating the Firmen. But now that you separate the Firmen tho it becomes the opp:
- ⇒ pos korrel found! ⇔ Je höher die Verantwortung, desto höher die Arbeitszufriedenheit
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=> MLMs solve the problem!
- ⇒ Why not just not use the MLM and instead just take the grand avg of the separate Firmen instead. (take the ausgezogene Linien and calc the grand avg line. skipping the MLM step)
- ⇒ can and does work (typically similar results as MLM). but theres infoverlust.
- thats why u should use MLM to keep all info
- eg: theres diff avg Verantw levels for each Firma
- ⇒ abh exists btw Firma and Verantw
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- eg Detkoeff of lin Reg (prediction acc)
Ecological Fallacy – Auf der Level-2 Ebene gefundene Zusammenhänge werden fälschlicherweise auf die Level-1 Ebene übertragen.
eg
- Why not we take the avg/mean of each Firma, and make a lin Reg.
- Durchschnittswerte pro Firma
- but now were looking at the avgs, meaning on another (upper) level.
- ⇒ no longer micro-micro, but macro-macro
- ⇒ Ecological Fallacy
- we in turn answer a diff q. Not the q that was asked (namely per person - micro, and not per firma - macro)
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- Imagine two neighborhoods:
- Neighborhood
- Uptown
- % College Graduates―80%
- Average Income―$100,000
- Midtown
- % College Graduates―40%
- Average Income―$50,000
- You might look at this and say:
- “People with more education earn more money.”
- But this is the ecological fallacy because you’re assuming that individuals with more education in the group are earning more, when all you actually know is that the group averages are correlated.
- 👉 What if, within each neighborhood, the highest earners are actually those without degrees? Then your individual-level assumption would be wrong, even though the group data suggested otherwise.
- what if the 20% that arent graduated are the ones with the most income! (eg self made men)
- ⇒ its those who didnt graudate with high incomes that pull the avg income of the city up, not the college grads - altho the city graduate ratio makes it look that way!
- findings: the more Einkommen, the more no votes for 13. AHV
- ⇒ again the case of Ecological Fallacy
- it only applies to level 2, macro grp pro Gemeinde
- and not level 1, pro person
- meaning q is diff. not the more Einkommen per person but, the more Einkommen per Gemeinde ⇒ the more no's to 13. AHV
- ⇒ again need MLM to consider grp size, etc etc. Alleviating Eco Fallacy
ICC
- ICC measures Abh = [0, 1]
- "Class" = "Klasse" = Level 2 = macro level = "Gruppen"
- Der ICC gibt im Wesentlichen an, wie gross die Varianz zwischen den Gruppen im Vergleich zur Varianz innerhalb der Gruppen ist.
ICC = 𝜌I
= Var_zw/(Var_zw+Var_inn)
= Var_zw/totaleVar
- ⇔ Var_zw ~= Var_inn ⇔ values inn einer Gruppe sind unabh
- since ICC very low ⇔ low abh (to which grp you belong ⇔ doesnt matter which grp/school you belong, the measurements are "fair") ⇔ "Unabh" ⇔ Unilevel models usable, MLM not necc
- low ICC ⇔ need more Messwdh to reach high Reliabilität
- if unabh/ICC = 0 u dont have to use MLM. U can tho
- But Unilevel models (the classic ANOVA and lin Regs) can be used. (since Unabh satsif as usual)
- ⇔ Var_zw >> Var_inn ⇔ values inn Gruppe sind ähnlich; general values of other grps are diff!
- ICC high ⇔ high Abh (towards which grp/school you belong )⇔ the means are diff placed ⇔ need MLM
- high ICC ⇔ need less Messwdh to reach high Reliabilität
Design Effect
- Design effect answers the following q:
- ⇔ to have the same Standardfehler SE as if doing it the unabh way/Unilevel model,
how much larger/by which factor (= "design effect") larger should my SP size be so that my MLM has the same precision/SE as the unabh way/Unilevel model?
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- ⇔ how often should i measure a var to see stability - no more Schwankungen (measurements lead to similar results) - measurement/result consistency
- eg, having one exam to eval math skills is not very realiable. since u dont see the consistency. 10 exams and then avg it is more realible than one exam's realiability
- same eg with Stimmung (has natural low Abh / ICC, since Stimmung very var at every moment)
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Reliabilität ( 𝜆j )
𝑛j = Gruppengrösse
- incr nj ⇒ decr sigma^2 ⇒ incr Realibilität to 1
- => better to have fewer but larger grps, than have many but small grps (same total SP size)
- ⇔ formula very sim to ICC formula