Please enable JavaScript.

Coggle requires JavaScript to display documents.

Stats pt2, 7 Feste Param & Modellspez, 8 Longitudinaldaten, 9 …

- - - - Beobachteter Wert = Was wirklich gemessen wurde
      - Gefitteter Wert = Was das Modell vorhergesagt hat
      - Residuum = Beobachtet – Gefittet→Das, was das Modell nicht erklären kann
    - - LL(M2) = -4,61 < -3,99 = LL(M1)
      - = 2*(LL(M1) - LL(M2))
        
        = 2*(-3,99 - (-4,61)) = 1,23
- - - - Informationskriterien = Modelgüte + Modellkomplexität = Devianz + a*q, for some a
      - ⇔ the more #param q, the more complex, the less good it is
      - IC = Information Criterion
    - - ⇒ the less #Param q, the smaller the AIC/BIC
    - - ln(Ntot) small ⇒ the more parsimonious (the smaller the BIC)
  - - - ⇒ AIC and BIC indicate that M2 is more parsimonious than M1
        
        (thus ses_Mean from M1 is not necc)
- - - - nbinges.i ⇔ #Essanfälle.weekNr
      - findings:
        
        ⇒
        Korrel > 0 ⇒ Daten Abh
        
        ⇒ the lower the Korrel, the weiter auseinander the Messwdh
        
        if this werent the case, we'd have a "Compound Symmetry" Muster
        
        - (gleich grosse Korrelationen, unabhängig vom zeitlichen Abstand der Messung).
        
        - "Compound Symmetry" Muster ⇔ Korrelkoeff = ICC
      - To check for the Korrel, you simply slap nbinges week i with nbinges week j in the same Streuudiag, and calc or see the Korrel:
- - - - Kovarianzen/Korrelationen zw the Faktorstufen müssen gleich gross sein!
        = req "Compound Symmetry" / "Sphericity"
        
        fiddle around with the df to correct imprecision
        
        df written as FWert_df1,df2
        
        ⇒ but pWert becomes grösser
        
        Korrekturfaktor HuynhFeldt Epsilon (e).
        
        - Huynh-Feldt Epsilon (ε):
        
        - It estimates how much the degrees of freedom should be reduced to correct for the sphericity/compund symmetry violation.
        
        eg: old df1 * ε = new df1
        
        //calc using the "Greenhouse-Geisser" Eps first, then converted to the HF Eps
        
        //calc of the GG Eps uses the sum of all diag values of the Kovarianzenmatrix
  - - - is sadly a condi in trad models!
- - - - Viele verschiedene Formen von Abhängigkeiten (Muster von Kovarianzmatrizen) können so via MLM modelliert werden!
- - - - Koeff y11 x predictor level 1 x predictor level 2
        
        Koeff y11 schätzt den Interaktionseffekt.
        
        for every predictor level 2 x.j incr by 1 Einheit,
        predictor level 1 incr by some Betrag y11
        (thus also incr the Zielvar Yij by the same Betrag obv..)
        
        ⇔ for every Einheit predictor level 2 incr, the Steigung of level 1 predictor incr/decr by value y11
        
        x.j++
        => y10++ by y11
        y11 = Interaktionseffekt
        
        //the larger the mean of one predictor, the lower the impact of the other predictor, kinda obv
        
        ⇒ eg if IQ is much more impactful than Feinmotorik for eg...
        
        if y11 is 0 ⇒ Modell E = Modell D = RIM with level 1 + 2 predictors
        
        if y01 or y10 = 0, then the other = y11?
      - 𝜸𝟏𝟎: Die Steigung des Zusammenhangs zwischen verbalem IQ und Lesekompetenz beträgt 2.48 in einer Klasse mit mittlerem SES=0 (=durchschnittlicher SES).
      - 𝜸𝟎𝟏: Die Steigung des Zusammenhangs zwischen mittlerem SES der Klasse und Lesekompetenz beträgt 0.15 für einE SchülerIn mit verbalem IQ=0 (=durchschnittlicher IQ).
    - - “Does the relationship between student IQ and reading proficiency depend on school climate?”
        
        IQ_centered (0.7): Within schools, higher individual IQ leads to higher reading proficiency.
        
        school_climate (1.5): Students in more positive climates tend to score higher, even with average IQ.
        
        Interaction (0.3): The effect of IQ on reading is stronger in better climates. This is your cross-level interaction.
        
        Intercept (45.0): Expected reading score when all predictors are zero.
        
        Variable Estimate Std.Error
        
        (Intercept) 45.0 1.1
        
        IQ_centered 0.7 0.1
        
        school_climate 1.5 0.4
        
        IQ_centered:school_climate 0.3 0.1
- - - - since grp mean centered now
      - thus the erk Varianz doesnt become smaller