Generalized Linear Models

Recall the linear model

\[y = \alpha + \beta x + \epsilon\]

Linear models are appropriate where the response variable (\(y\)) is continuous and the errors (\(\epsilon\)) are normally distributed. Many experimental designs (for example, case-control) have categorical outcomes and/or outcomes whose errors are not normally distributed. Often, these experiments may be modeled with a more general category of models called ‘generalized linear models’ (or GLMs).

To understand GLMs, we need to be more precise about what our linear regression is actually doing. We are really saying:

\[y = \mu + \epsilon\]

or equivalently

\[\mathbb{E}(Y|x) = \mu = \alpha + \beta x\]

That is, our model is specifying the conditional expectation of observations \(Y\) on the idependent variable \(x\). In particular, that expectation is linear.

What Happens When \(\mathbb{E}(Y|x)\) is Not Linear?

A natural question to ask is: Can we find a function of the expectation that is linear? We would like this function to be invertible, so that we are really just transforming things. The answer is ‘yes’ - if - we assume that \(Y\) has a distribution that is part of the ‘exponential family’.

This family has the following form (note - this is vector notation)

\[f_Y(y|\theta) = h(y) g(\theta)exp(\eta(\theta)\cdot T(x))\]

Kinda ugly, but also pretty general. Note that the normal distribution is in this family! So is the binomial, negative binomial, Poisson, Gamma,...

Model

Suppose our outcome variable \(Y\) has a distribution in the exponential family. We need an invertible function \(g\) so that:

\[\mathbb{E}(Y|x) = \mu = g^{-1}(\alpha + \beta x)\]

Why???

Because when we apply \(g\) to the expectation:

\[g(\mu) = g(g^{-1}(\alpha + \beta x))\]

a miracle occurs...

\[g(\mu) = \alpha + \beta x\]

Because it has miraculous properties, we give \(g\) a name: \(g\) is called a ‘link’ function. It ‘links’ the conditional expectation of our outcome variable to a linear function. Everybody loves linear functions! Yay!

Now, DESeq2 uses a negative binomial model, and we’ll talk about that - but first lets look at a model that is commonly used in case-control type settings.

Logistic Regression

In logistic regression, we model the probability of the outcome \(y\), given the independent variable \(x\). That is, \(Y|x\) is Bernoulli, with success probability \(p\) given by:

\[\mathbb{E}(Y|x) = p = \frac{1}{1+e^{-(\alpha + \beta x)}}\]

Note that \(p\) is bounded between \(0\) and \(1\) and is defined for all values of \(\alpha + \beta x\).

We use the notation \(expit(t)\) to denote the following:

\[expit(t) = \frac{1}{1+e^{-t}}\]

\(expit\) is known as the logistic function.

and \(logit(t)\) to denote:

\[logit(t) = \log\left(\frac{1}{1-t}\right)\]

Note that:

\[logit(expit(t)) = t\]

so that

\[logit(p) = \alpha + \beta x\]

Because \(logit(p) = logit(\mathbb{E}(Y|x))\), it is called the link function.

expit<-function(t){
    return(1/(1+exp(-t)))
}
x<-expit((-10:10))
plot(x)
_images/LogisticRegression_13_0.png

So, how do we perform a logistic regression in R? First, let’s get a data set:

Titanic<-read.csv("titanic.csv")
attach(Titanic)
#Titanic
library(plyr)
Titanic$pclass<-revalue(pclass, c("1st"=1, "2nd"=1,"3rd"=0))
Titanic
The following objects are masked from Titanic (pos = 4):

    age, boat, embarked, home.dest, name, pclass, room, row.names, sex,
    survived, ticket
row.namespclasssurvivednameageembarkedhome.destroomticketboatsex
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4410Allison, Mrs Hudson J.C. (Bessie Waldo Daniels)25SouthamptonMontreal, PQ / Chesterville, ONC26female
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101010Artagaveytia, Mr Ramon71CherbourgMontevideo, Uruguay(22)male
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171710Baxter, Mr Quigg Edmond24CherbourgMontreal, PQB-58/60male
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191911Beckwith, Mr Richard Leonard37SouthamptonNew York, NYD-355male
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212111Behr, Mr Karl Howell26CherbourgNew York, NYC-1485male
222210Birnbaum, Mr Jakob25CherbourgSan Francisco, CA(148)male
232311Bishop, Mr Dickinson H.25CherbourgDowagiac, MIB-497male
242411Bishop, Mrs Dickinson H. (Helen Walton)19CherbourgDowagiac, MIB-497female
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262610Blackwell, Mr Stephen Weart45SouthamptonTrenton, NJ(241)male
272711Blank, Mr Henry39CherbourgGlen Ridge, NJA-317male
282811Bonnell, Miss Caroline30SouthamptonYoungstown, OHC-78female
292911Bonnell, Miss Elizabeth58SouthamptonBirkdale, England Cleveland, OhioC-1038female
303010Borebank, Mr John JamesNASouthamptonLondon / Winnipeg, MBD-21/2male
313111Bowen, Miss Grace Scott45CherbourgCooperstown, NY4female
323211Bowerman, Miss Elsie Edith22SouthamptonSt Leonards-on-Sea, England Ohio6female
333311Bradley, Mr GeorgeNASouthamptonLos Angeles, CA15male
343410Brady, Mr John Bertram41SouthamptonPomeroy, WAmale
353510Brandeis, Mr Emil48CherbourgOmaha, NE17591 L50 9s 11d(208)male
363610Brewe, Dr Arthur JacksonNACherbourgPhiladelphia, PAmale
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383811Brown, Mrs John Murray (Caroline Lane Lamson)59SouthamptonBelmont, MAC-101Dfemale
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404010Butt, Major Archibald Willingham45SouthamptonWashington, DCmale
414111Calderhead, Mr Edward P.NASouthamptonNew York, NY5/7male
424211Candee, Mrs Edward (Helen Churchill Hungerford)53CherbourgWashington, DC6female
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505011Carter, Miss Lucile Polk14SouthamptonBryn Mawr, PA4female
515111Carter, Master William T. II11SouthamptonBryn Mawr, PA4male
525210Case, Mr Howard Brown49SouthamptonAscot, Berkshire / Rochester, NYmale
535311Cassebeer, Mrs Henry Arthur jr (Genevieve Fosdick)NACherbourgNew York, NY5female
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565610Chaffee, Mr Herbert Fuller46SouthamptonAmenia, NDmale
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585811Chambers, Mr Norman Campbell27SouthamptonNew York, NY / Ithaca, NY5male
595911Chambers, Mrs Norman Campbell (Bertha Griggs)31SouthamptonNew York, NY / Ithaca, NY5female
606011Cherry, Miss GladysNASouthamptonLondon, England8female
616111Chevre, Mr PaulNACherbourgParis, France7male
626211Chibnall (Bowerman), Mrs Edith MarthaNASouthamptonSt Leonards-on-Sea, England Ohio6female
636310Chisholm, Mr Roderick RobertNALiverpool, England / Belfastmale
646410Clark, Mr Walter Miller27CherbourgLos Angeles, CAC-87male
656511Clark, Mrs Walter Miller (Virginia McDowell)26CherbourgLos Angeles, CAC-874female
666610Clifford, Mr George QuincyNASouthamptonStoughton, MAmale
676710Colley, Mr Edward PomeroyNASouthamptonVictoria, BCmale
686811Compton, Mrs Alexander Taylor (Mary Eliza Ingersoll)64CherbourgLakewood, NJ14female
696910Compton, Mr Alexander Taylor, Jr37CherbourgLakewood, NJmale
707011Compton, Miss Sara Rebecca39CherbourgLakewood, NJ14female
717111Cornell, Mrs Robert Clifford (Malvina Helen Lamson)55SouthamptonNew York, NYC-1012female
727210Crafton, Mr John BertramNASouthamptonRoachdale, INmale
737310Crosby, Captain Edward Gifford70SouthamptonMilwaukee, WI(269)male
747411Crosby, Mrs Edward Gifford (Catherine Elizabeth Halstead)69SouthamptonMilwaukee, WI5female
757511Crosby, Miss Harriet R.36SouthamptonMilwaukee, WI5female
767610Cumings, Mr John Bradley39CherbourgNew York, NYC-85male
777711Cumings, Mrs John Bradley (Florence Briggs Thayer)38CherbourgNew York, NYC-854female
787811Daly, Mr Peter Denis NASouthamptonLima, PeruAmale
797911Daniel, Mr Robert Williams27SouthamptonPhiladelphia, PA7male
808010Davidson, Mr Thornton31SouthamptonMontreal, PQmale
818111Davidson, Mrs Thornton (Orian Hays)27SouthamptonMontreal, PQ3female
828211de Villiers, Madame BertheNACherbourgBelgium Montreal, PQ6female
838311Dick, Mr Albert Adrian31CherbourgCalgary, AB3male
848411Dick, Mrs Albert Adrian Vera Gillespie17CherbourgCalgary, AB3female
858511Dodge, Dr. WashingtonNASouthamptonSan Francisco, CA13male
868611Dodge, Mrs Washington (Ruth Vidaver)NASouthamptonSan Francisco, CA5/7female
878711Dodge, Master Washington4SouthamptonSan Francisco, CA5/7male
888811Douglas, Mrs Frederick Charles (Suzette Baxter)27CherbourgMontreal, PQ6female
898910Douglas, Mr Walter Donald50CherbourgDeephaven, MN / Cedar Rapids, IA(62)male
909011Douglas, Mrs Walter Donald (Mahala Dutton)48CherbourgDeephaven, MN / Cedar Rapids, IA2female
919111Duff Gordon, Sir Cosmo Edmund49CherbourgLondon / Paris11755 L39 12s1male
929211Duff Gordon, Lady (Lucille Wallace Sutherland)48CherbourgLondon / Paris17485 L56 18s 7d1female
939310Dulles, Mr William Crothers39CherbourgPhiladelphia, PA(133)male
949411Earnshaw, Mrs Boulton (Olive Potter)23CherbourgMt Airy, Philadelphia, PA7female
959511Eustis, Miss Elizabeth Mussey53CherbourgBrookline, MA4female
969610Evans, Miss Edith Corse36CherbourgNew York, NYfemale
979711Flegenheim, Mrs Alfred (Antoinette)NACherbourgNew York, NY7female
989811Flynn, Mr John IrvingNASouthamptonBrooklyn, NY5/7male
999910Foreman, Mr Benjamin Laventall30CherbourgNew York, NYmale
10010011Fortune, Miss Alice Elizabeth24SouthamptonWinnipeg, MB10female
10110110Fortune, Mr Charles Alexander19SouthamptonWinnipeg, MBmale
10210211Fortune, Miss Ethel Flora28SouthamptonWinnipeg, MB10female
10310311Fortune, Miss Mabel23SouthamptonWinnipeg, MB10female
10410410Fortune, Mr Mark64SouthamptonWinnipeg, MBmale
10510511Fortune, Mrs Mark (Mary McDougald)60SouthamptonWinnipeg, MB10female
10610610Franklin, Mr Thomas ParhamNASouthamptonWestcliff-on-Sea, Essexmale
10710711Frauenthal, Dr Henry William49CherbourgNew York, NY5male
10810811Frauenthal, Mrs Henry William (Clara Heinsheimer)NACherbourgNew York, NY5female
10910911Frauenthal, Mr Isaac Gerald44SouthamptonNew York, NY5male
11011011Frolicher, Miss Marguerite22CherbourgZurich, Switzerland5female
11111111Frolicher-Stehli, Mr Maxmillian60CherbourgZurich, Switzerland5male
11211211Frolicher-Stehli, Mrs Maxmillian (Margaretha Emerentia Stehli)48CherbourgZurich, Switzerland5female
11311310Futrelle, Mr Jacques37SouthamptonScituate, MAmale
11411411Futrelle, Mrs Jacques (May Peel)35SouthamptonScituate, MA9female
11511510Gee, Mr Arthur H.47SouthamptonSt Anne's-on-Sea, Lancashire(275)male
11611611Gibson, Miss Dorothy22CherbourgNew York, NY7female
11711711Gibson, Mrs Leonard (Pauline C. Boeson)45CherbourgNew York, NY7female
11811811Goldenberg, Mr Samuel L.49CherbourgParis, France / New York, NY5male
11911911Goldenberg, Mrs Samuel L. (Edwiga Grabowsko)NACherbourgParis, France / New York, NY5female
12012010Goldschmidt, Mr George B.71CherbourgNew York, NYmale
12112111Gracie, Colonel Archibald IV54SouthamptonWashington, DCC-51113780 L28 10sBmale
12212210Graham, Mr George Edward38SouthamptonWinnipeg, MB(147)male
12312311Graham, Miss Margaret Edith19SouthamptonGreenwich, CTC-12517582 L153 9s 3d3female
12412411Graham, Mrs William Thompson (Edith Junkins)58SouthamptonGreenwich, CTC-9117582 L153 9s 3d3female
12512511Greenfield, Mrs Leo David (Blanche Strouse)45CherbourgNew York, NY7female
12612611Greenfield, Mr William Bertram23CherbourgNew York, NY7male
12712710Guggenheim, Mr Benjamin46CherbourgNew York, NYB-82/417593 L56 18s 7dmale
12812811Harder, Mr George Achilles25CherbourgBrooklyn, NY5male
12912911Harder, Mrs George Achilles (Dorothy Annan)21CherbourgBrooklyn, NY5female
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13113111Harper, Mrs Henry Sleeper (Myna Haxtun)49CherbourgNew York, NY3female
13213210Harris, Mr Henry Birkhardt45SouthamptonNew York, NYC-8336973 L83 9s 6dmale
13313311Harris, Mrs Henry Birkhardt (Irene Wallach)36SouthamptonNew York, NYC-8336973 L83 9s 6dDfemale
13413411Hawksford, Mr Walter JamesNASouthamptonKingston, Surrey3male
13513510Hays, Mr Charles Melville55SouthamptonMontreal, PQ(307)male
13613611Hays, Mrs Charles Melville (Clara Jennings Gregg)52SouthamptonMontreal, PQ3female
13713711Hays, Miss Margaret Bechstein24SouthamptonNew York, NY7female
13813810Head, Mr ChristopherNASouthamptonLondon / Middlesexmale
13913910Hilliard, Mr Herbert HenryNASouthamptonBrighton, MAmale
14014010Hipkins, Mr William EdwardNASouthamptonLondon / Birminghammale
14114111Hippach, Miss Jean Gertrude16CherbourgChicago, ILB-18111361 L57 19s 7d4female
14214211Hippach, Mrs Louis Albert (Ida Sophia Fischer)44CherbourgChicago, ILB-18111361 L57 19s 7d4female
14314311Hogeboom, Mrs John C. (Anna Andrews)51SouthamptonHudson, NYD-?13502 L7710female
14414410Holverson, Mr Alexander Oskar42SouthamptonNew York, NY(38)male
14514511Holverson, Mrs Alexander Oskar (Mary Aline Towner)35SouthamptonNew York, NYfemale
14614611Homer, Mr Harry35CherbourgIndianapolis, IN15male
14714711Hoyt, Mr Frederick Maxfield38SouthamptonNew York, NY / Stamford CTC-93Dmale
14814811Hoyt, Mrs Frederick Maxfield (Jane Anne Forby)35SouthamptonNew York, NY / Stamford CTC-93Dfemale
14914910Hoyt, Mr William F.NACherbourgNew York, NY14male
15015010Isham, Miss Anne Elizabeth50CherbourgParis, France New York, NYC-49female
15115111Ismay, Mr Joseph Bruce49SouthamptonLiverpoolB-52/4/6112058 ComplimentaryCmale
15215210Jones, Mr Charles Cresson46SouthamptonBennington, VT(80)male
15315310Julian, Mr Henry ForbesNASouthamptonLondonmale
15415410Kent, Mr Edward Austin58CherbourgBuffalo, NY(258)male
15515510Kenyon, Mr Frederick R.41SouthamptonSouthington / Noank, CTmale
15615611Kenyon, Mrs Frederick R. (Marion)NASouthamptonSouthington / Noank, CT8female
15715711Kimball, Mr Edwin Nelson Jr.42SouthamptonBoston, MA5male
15815811Kimball, Mrs Edwin Nelson Jr. (Gertrude Parsons)40SouthamptonBoston, MA5female
15915910Klaber, Mr HermanNASouthamptonPortland, ORmale
16016011Leader, Dr Alice FarnhamNASouthamptonNew York, NY8female
16116110Lewy, Mr Ervin G.NACherbourgChicago, ILmale
16216210Lindeberg-Lind, Mr Erik Gustaf42SouthamptonStockholm, Swedenmale
16316311Lindstrom, Mrs Carl Johan (Sigrid Posse)55CherbourgStockholm, Sweden6female
16416411Lines, Mrs Ernest H. (Elizabeth Lindsey James)50CherbourgParis, France9female
16516511Lines, Miss Mary Conover16CherbourgParis, France9female
16616610Lingrey, Mr EdwardNAmale
16716710Long, Mr Milton Clyde29SouthamptonSpringfield, MA(126)male
16816811Longley, Miss Gretchen Fiske21SouthamptonHudson, NYD-?13502 L7710female
16916910Loring, Mr Joseph Holland30SouthamptonLondon / New York, NYmale
17017011Madill, Miss Georgette Alexandra15SouthamptonSt Louis, MOB-524160 L2212female
17117110Maguire, Mr John Edward30SouthamptonBrockton, MAmale
17217211Marechal, Mr PierreNACherbourgParis, France7male
17317310Marvin, Mr Daniel WarnerNASouthamptonNew York, NYmale
17417411Marvin, Mrs Daniel Warner (Mary Graham Carmichael Farquarson)NASouthamptonNew York, NYfemale
17517510McCaffry, Mr Thomas Francis46CherbourgVancouver, BC(292)male
17617610McCarthy, Mr Timothy J.54SouthamptonDorchester, MA(175)male
17717711McGough, Mr James R.36SouthamptonPhiladelphia, PA7male
17817810Meyer, Mr Edgar Joseph28CherbourgNew York, NYmale
17917911Meyer, Mrs Edgar Joseph (Leila Saks)NACherbourgNew York, NY6female
18018010Millet, Mr Francis Davis65SouthamptonEast Bridgewater, MA(249)male
18118111Minahan, Miss Daisy E.33QueenstownGreen Bay, WI14female
18218210Minahan, Dr William Edward44QueenstownFond du Lac, WI(230)male
18318311Minahan, Mrs William Edward (Lillian E. Thorpe)37QueenstownFond du Lac, WI14female
18418411Mock, Mr Philip E.NACherbourgNew York, NY11male
18518510Molson, Mr Harry Markland55SouthamptonMontreal, PQmale
18618610Moore, Mr Clarence Bloomfield47SouthamptonWashington, DCmale
18718710Natsch, Mr Charles H.36CherbourgBrooklyn, NYmale
18818810Newell, Mr Arthur Webster58CherbourgLexington, MA(122)male
18918911Newell, Miss Madeleine31CherbourgLexington, MA6female
19019011Newell, Miss Marjorie23CherbourgLexington, MA6female
19119111Newsom, Miss Helen Monypeny19SouthamptonNew York, NY5female
19219210Nicholson, Mr Arthur Ernest64SouthamptonIsle of Wight, England(263)male
19319311Omont, Mr A. FernandNACherbourgParis, France7male
19419410Ostby, Mr Engelhart Cornelius64CherbourgProvidence, RI(234)male
19519511Ostby, Miss Helen Raghnild22CherbourgProvidence, RI5female
19619610Ovies y Rodriguez, Mr Servando28?Havana, Cuba(189)male
19719710Parr, Mr William Henry MarshNABelfastmale
19819810Partner, Mr AustinNASouthamptonSurbiton Hill, Surrey(166)male
19919910Payne, Mr Vivian Ponsonby22SouthamptonMontreal, PQmale
20020010Pears, Mr ThomasNASouthamptonIsleworth, Englandmale
20120111Pears, Mrs Thomas (Edith)NASouthamptonIsleworth, England8female
20220210Penasco, Mr Victor de Satode18CherbourgMadrid, Spainmale
20320311Penasco, Mrs Victor de Satode (Josefa de Soto)17CherbourgMadrid, Spain8female
20420411Peuchen, Major Arthur Godfrey52SouthamptonToronto, ONC-1046male
20520510Porter, Mr Walter Chamberlain46SouthamptonWorcester, MA(207)male
20620611Potter, Mrs Thomas, Jr. (Lily Alexenia Wilson)56CherbourgMt Airy, Philadelphia, PA7female
20720710Reuchlin, Jonkheer John GeorgeNASouthamptonRotterdam, Netherlandsmale
20820811Rheims, Mr George LucienNACherbourgParis / New York, NY17604 L39 12sAmale
20920911Robert, Mrs Edward Scott (Elisabeth Walton McMillan)43SouthamptonSt Louis, MOB-324160 L2212female
21021010Roebling, Mr Washington Augustus 2nd31SouthamptonTrenton, NJmale
21121111Romaine, Mr Charles HallaceNASouthamptonNew York, NY15male
21221210Rood, Mr Hugh R.NASouthamptonSeattle, WAmale
21321311Rosenbaum (Russell), Miss Edith Louise33CherbourgParis, FranceA-1117613 L27 14s 5d11female
21421410Ross, Mr John HugoNACherbourgWinnipeg, MBmale
21521511Rothes, the Countess of (Noel Lucy Martha Dyer-Edwardes)27SouthamptonLondon Vancouver, BC8female
21621610Rothschild, Mr Martin55CherbourgNew York, NYmale
21721711Rothschild, Mrs Martin (Elizabeth L. Barrett)54CherbourgNew York, NY6female
21821810Rowe, Mr Alfred G.NASouthamptonLondon(109)male
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22122111Ryerson, Miss Emily Borie18CherbourgHaverford, PA / Cooperstown, NY17608 L262 7s 6d4female
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22422411Saalfeld, Mr AdolpheNASouthamptonManchester, England3male
22522511Salomon, Mr Abraham L.NASouthamptonNew York, NY1male
22622611Schabert, Mrs Paul (Emma Mock)NACherbourgNew York, NY11female
22722711Seward, Mr Frederic Kimber34SouthamptonNew York, NY7male
22822811Shutes, Miss Elizabeth W.40SouthamptonNew York, NY / Greenwich CTC-12517582 L153 9s 3d3female
22922911Silverthorne, Mr Spencer Victor36SouthamptonSt Louis, MO5male
23023010Silvey, Mr William Baird50Duluth, MNmale
23123111Silvey, Mrs William Baird (Alice Munger)39Duluth, MNfemale
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23323311Sloper, Mr William Thompson28SouthamptonNew Britain, CT7male
23423410Smart, Mr John Montgomery56SouthamptonNew York, NYmale
23523510Smith, Mr James Clinch56CherbourgSt James, Long Island, NYmale
23623610Smith, Mr Lucien Philip24SouthamptonHuntington, WVmale
23723711Smith, Mrs Lucien Philip (Mary Eloise Hughes18SouthamptonHuntington, WV6female
23823810Smith, Mr Richard WilliamNASouthamptonStreatham, Surreymale
23923911Snyder, Mr John Pillsbury24SouthamptonMinneapolis, MN7male
24024011Snyder, Mrs John Pillsbury (Nelle Stevenson)23SouthamptonMinneapolis, MN7female
24124111Spedden, Mr Frederick Oakley45CherbourgTuxedo Park, NY3male
24224211Spedden, Mrs Frederick Oakley (Margaretta Corning Stone)40CherbourgTuxedo Park, NY3female
24324311Spedden, Master Robert Douglas6CherbourgTuxedo Park, NY3male
24424410Spencer, Mr William Augustus57CherbourgParis, Francemale
24524511Spencer, Mrs William Augustus (Marie Eugenie)NACherbourgParis, France6female
24624611Staehlin, Dr Max32CherbourgBasel, Switzerland3male
24724710Stead, Mr William Thomas62SouthamptonWimbledon Park, London / Hayling Island, HantsC-89male
24824811Stengel, Mr Charles Emil Henry54CherbourgNewark, NJ1male
24924911Stengel, Mrs Charles Emil Henry (Annie May Morris)43CherbourgNewark, NJ5female
25025011Stephenson, Mrs Walter Bertram (Martha Eustis)52Haverford, PA4female
25125110Stewart, Mr Albert A.NACherbourgGallipolis, Ohio / ? Paris / New Yorkmale
25225211Stone, Mrs George Nelson (Martha E.)62Cincinatti, OH6female
25325310Straus, Mr Isidor67SouthamptonNew York, NY17483 L221 15s 7d(96)male
25425410Straus, Mrs Isidor (Ida Blun)63SouthamptonNew York, NY17483 L221 15s 7dfemale
25525510Sutton, Mr Frederick61SouthamptonHaddenfield, NJ(46)male
25625611Swift, Mrs Frederick Joel (Margaret Welles Barron)46SouthamptonBrooklyn, NY8female
25725710Taussig, Mr Emil52SouthamptonNew York, NYmale
25825811Taussig, Mrs Emil (Tillie Mandelbaum)39SouthamptonNew York, NY8female
25925911Taussig, Miss Ruth18SouthamptonNew York, NY8female
26026011Taylor, Mr Elmer Zebley48SouthamptonLondon / East Orange, NJC-1265male
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26226210Thayer, Mr John Borland49CherbourgHaverford, PAmale
26326311Thayer, Mrs John Borland (Marian Longstreth Morris)39CherbourgHaverford, PA4female
26426411Thayer, Mr John Borland, jr.17CherbourgHaverford, PABmale
26526510Thorne, Mr George (alias of: Mr George Rosenshine)46CherbourgNew York, NYmale
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26826810Uruchurtu, Mr Manuel E.NACherbourgMexico City, Mexicomale
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27027010Walker, Mr William Anderson47SouthamptonEast Orange, NJmale
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27327310Weir, Col John60SouthamptonEngland Salt Lake City, Utahmale
27427411White, Mrs J. Stuart (Ella Holmes)55CherbourgNew York, NY / Briarcliff Manor NY8female
27527510White, Mr Percival Wayland54SouthamptonBrunswick, MEmale
27627610White, Mr Richard Frasar21SouthamptonBrunswick, ME(169)male
27727710Wick, Mr George Dennick57SouthamptonYoungstown, OHmale
27827811Wick, Mrs George Dennick (Martha Hitchcock)45SouthamptonYoungstown, OH8female
27927911Wick, Miss Mary Natalie31SouthamptonYoungstown, OHC-78female
28028010Widener, Mr George Dunton50CherbourgElkins Park, PAmale
28128111Widener, Mrs George Dunton (Eleanor Elkins)50CherbourgElkins Park, PA4female
28228210Widener, Mr Harry Elkins27CherbourgElkins Park, PAmale
28328311Willard, Miss Constance20SouthamptonDuluth, MNfemale
28428410Williams, Mr Charles Duane51CherbourgGeneva, Switzerland / Radnor, PAmale
28528510Williams, Mr Fletcher LambertNASouthamptonLondon, Englandmale
28628611Williams, Mr Richard Norris II21CherbourgGeneva, Switzerland / Radnor, PAAmale
28728711Woolner, Mr HughNASouthamptonLondon, EnglandDmale
28828810Wright, Mr GeorgeNASouthamptonHalifax, NSmale
28928911Young, Miss Marie Grice36CherbourgNew York, NY / Washington, DC8female
29029011Barber, Ms NASouthamptonfemale
29129111Bazzani, Ms AlbinaNACherbourgfemale
29229211Bidois, Miss RosalieNACherbourg17754female
29329311Bird, Ms EllenNASouthamptonC-9717483female
29429411Bissetti, Ms AmeliaNACherbourgC-99female
29529511Burns, Ms Elizabeth MargaretNACherbourgfemale
29629611Chaudanson, Ms VictorineNACherbourg17608female
29729711Cleaver, Ms AliceNASouthamptonC2211female
29829811Daniels, Ms SarahNASouthamptonC-228female
29929911Endres, Miss Caroline LouiseNACherbourgNew York, NYC-4517754 L224 10s 6d4female
30030010Farthing, Mr JohnNASouthamptonC-55 (?C-95)17483male
30130110Fleming, Ms MargaretNACherbourg4female
30230211Francatelli, Ms Laura MabelNACherbourg17485female
30330310Fry, Mr RichardNASouthamptonB-102112058male
30430411Geiger, Miss Emily NACherbourgfemale
30530510Giglio, Mr VictorNACherbourgB-8617593male
30630610Harrington, Mr CharlesNASouthamptonmale
30730710Harrison, Mr William Henry40Southampton112059(110)male
30830810Hassah, Mr HamadNACherbourgmale
30930911Icabad (Icabod), MsNAfemale
31031010Keeping, Mr Edwin32Cherbourg(45)male
31131111Kenchen, Ms AmeliaNASouthampton2female
31231211LeRoy, Miss BertheNACherbourg2female
31331310Lesneur, Mr GustaveNACherbourgB-?male
31431411Maloney, MsNASouthampton8female
31531510Oliva, MlleNACherbourgfemale
31631611Pericault, MsNASouthamptonfemale
31731710Ringhini, Mr Sante33Cherbourg(232)male
31831810Robbins, Mr VictorNACherbourgC-6217754male
31931911Segesser, Mlle. EmmaNACherbourgfemale
32032010Seredeca, MsNASouthamptonfemale
32132110Ward, Ms AnnaNACherbourgfemale
32232211Wilson, Ms HelenNACherbourgfemale
32332310Abelson, Mr Samuel30CherbourgRussia New York, NYmale
32432411Abelson, Mrs Samuel (Anna)28CherbourgRussia New York, NY12female
32532510Andrew, Mr Edgar Samuel18SouthamptonBuenos Aires, Argentina / New Jersey, NJmale
32632610Andrew, Mr FrankNASouthamptonCornwall, England Houghton, MImale
32732710Angle, Mr William A.34SouthamptonWarwick, Englandmale
32832811Angle, Mrs William A. (Florence)32SouthamptonWarwick, Englandfemale
32932910Ashby, Mr John57SouthamptonWest Hoboken, NJmale
33033010Bailey, Mr Percy Andrew18SouthamptonPenzance, Cornwall / Akron, OHmale
33133110Baimbrigge, Mr Charles R.23SouthamptonGuernseymale
33233211Balls, Mrs Ada E. Hall36SouthamptonBristol, Avon / Jacksonville, FLfemale
33333310Banfield, Mr Frederick J.28SouthamptonPlymouth, Dorset / Houghton, MImale
33433410Bateman, Rev Robert James51SouthamptonJacksonville, FL(174)male
33533511Beane, Mr Edward32SouthamptonNorwich / New York, NYmale
33633611Beane, Mrs Edward (Ethel Clarke)19SouthamptonNorwich / New York, NYfemale
33733710Beauchamp, Mr Henry James28SouthamptonEnglandmale
33833811Becker, Mrs Allen Oliver (Nellie E. Baumgardner)36SouthamptonGuntur, India / Benton Harbour, MI230136 L3911female
33933911Becker, Miss Marion Louise4SouthamptonGuntur, India / Benton Harbour, MI230136 L3911female
34034011Becker, Master Richard F.1SouthamptonGuntur, India / Benton Harbour, MI230136 L3911male
34134111Becker, Miss Ruth Elizabeth12SouthamptonGuntur, India / Benton Harbour, MI230136 L3913female
34234211Beesley, Mr Lawrence34SouthamptonLondonD-56248698 L1313male
34334311Bentham, Miss Lilian W.19SouthamptonRochester, NY12female
34434410Berriman, Mr William S.23SouthamptonSt Ives, Cornwall / Calumet, MImale
34534510Botsford, Mr William Hull26SouthamptonElmira, NY / Orange, NJmale
34634610Bowenur, Mr SolomonNASouthamptonLondonmale
34734710Bracken, Mr James H.27SouthamptonLake Arthur, Chavez County, NMmale
34834811Brown, Miss Edith E.15SouthamptonCape Town, South Africa / Seattle, WA14female
34934910Brown, Mr Thomas William Solomon45SouthamptonCape Town, South Africa / Seattle, WAmale
35035011Brown, Mrs Thomas William Solomon (Elizabeth C.)40SouthamptonCape Town, South Africa / Seattle, WA14female
35135111Bryhl, Miss Dagmar20SouthamptonSkara, Sweden / Rockford, IL12female
35235210Bryhl, Mr Kurt Arnold Gottfrid25SouthamptonSkara, Sweden / Rockford, ILmale
35335311Buss, Miss Kate36SouthamptonSittingbourne, England / San Diego, CAE-?278499female
35435410Butler, Mr Reginald Fenton25SouthamptonSouthsea, Hants(97)male
35535510Byles, Rev. Thomas Roussel D.NASouthamptonLondonmale
35635611Bystrom, Mrs Carolina42SouthamptonNew York, NYfemale
35735711Caldwell, Mr Albert Francis26SouthamptonBangkok, Thailand / Roseville, IL13male
35835811Caldwell, Mrs Albert Francis (Sylvia Mae Harbaugh)26SouthamptonBangkok, Thailand / Roseville, IL13female
35935911Caldwell, Master Alden Gates0.8333SouthamptonBangkok, Thailand / Roseville, IL13male
36036011Cameron, Miss Clear31SouthamptonMamaroneck, NYfemale
36136110Campbell, Mr WilliamNABelfastmale
36236210Carbines, Mr William19SouthamptonSt Ives, Cornwall / Calumet, MI(18)male
36336310Carter, Rev Ernest Courtenay54SouthamptonLondonmale
36436410Carter, Mrs Ernest Courtenay (Lillian Hughes)44SouthamptonLondonfemale
36536510Chapman, Mr Charles Henry52SouthamptonBronx, NY(130)male
36636610Chapman, Mr John Henry30SouthamptonCornwall / Spokane, WA(17)male
36736710Chapman, Mrs John Henry (Elizabeth Lawry)30SouthamptonCornwall / Spokane, WAfemale
36836811Christy, Mrs Alice FrancesNASouthamptonLondonfemale
36936911Christy, Miss JulieNASouthamptonLondonfemale
37037010Clarke, Mr Charles V.29SouthamptonEngland / San Francisco, CAmale
37137111Clarke, Mrs Charles V. (Ada Maria)NASouthamptonEngland / San Francisco, CA14female
37237210Coleridge, Mr Reginald Charles29SouthamptonHartford, Huntingdonshiremale
37337310Collander, Mr Erik27SouthamptonHelsinki, Finland Ashtabula, Ohiomale
37437411Collett, Mr Sidney C. Stuart24SouthamptonLondon / Fort Byron, NY9male
37537510Collyer, Mr Harvey35SouthamptonBishopstoke, Hants / Fayette Valley, IDmale
37637611Collyer, Mrs Harvey (Charlotte Tate)31SouthamptonBishopstoke, Hants / Fayette Valley, ID14female
37737711Collyer, Miss Marjorie8SouthamptonBishopstoke, Hants / Fayette Valley, ID14female
37837810Cook, Mrs Selena Rogers22SouthamptonPennsylvaniaF-3314female
37937910Corbett, Mrs Walter H. (Irene Colvin)30SouthamptonProvo, UTfemale
38038010Corey, Mrs Percy C. (Mary Phyllis Elizabeth Miller)NASouthamptonUpper Burma, India Pittsburgh, PAfemale
38138110Cotterill, Mr Harry20SouthamptonPenzance, Cornwall / Akron, OHmale
38238210Cunningham, Mr Alfred FlemingNABelfastmale
38338310Davies, Mr Charles Henry21SouthamptonLyndhurst, Englandmale
38438411Davis, Mrs Agnes49SouthamptonSt Ives, Cornwall / Hancock, MIfemale
38538511Davis, Master John Morgan8SouthamptonSt Ives, Cornwall / Hancock, MImale
38638611Davis, Miss Mary28SouthamptonLondon / Staten Island, NY13female
38738710Deacon, Mr Percy18Southamptonmale
38838810de Brito, Mr Jose JoaquimNAPortugal / Sau Paulo, Brazilmale
38938910del Carlo, Mr Sebastiano28CherbourgLucca, Italy / California(295)male
39039011del Carlo, Mrs Sebastiano (Argenia Genovese)22CherbourgLucca, Italy / Californiafemale
39139110Denbury, Mr Herbert25SouthamptonGuernsey / Elizabeth, NJmale
39239210Dibden, Mr William18SouthamptonNew Forest, Englandmale
39339311Doling, Mrs Ada32SouthamptonSouthamptonfemale
39439411Doling, Miss Elsie18SouthamptonSouthamptonfemale
39539510Downton (?Douton), Mr William JamesNASouthamptonHolley, NYmale
39639610Drew, Mr James Vivian42SouthamptonGreenport, NY28220 L32 10smale
39739711Drew, Mrs James Vivian (Lulu Thorne Christian)34SouthamptonGreenport, NY28220 L32 10sfemale
39839811Drew, Master Marshall Brines8SouthamptonGreenport, NY28220 L32 10smale
39939911Duran y More, Miss AsuncionNACherbourgBarcelona, Spain / Havana, Cuba12female
40040011Duran y More, Miss FlorentinaNACherbourgBarcelona, Spain / Havana, Cuba12female
40140110Eitemiller, Mr George Floyd23SouthamptonEngland / Detroit, MImale
40240210Enander, Mr Ingvar21SouthamptonGoteborg, Sweden / Rockford, ILmale
40340310Fahlstrom, Mr Arne Jonas19SouthamptonOslo, Norway Bayonne, NJmale
40440410Faunthorpe, Mr HarryNASouthamptonEngland / Philadelphia, PA(286)male
40540511Faunthorpe, Mrs Lizzie (see Wilkinson, E.)NAfemale
40640610Fillbrook, Mr CharlesNASouthamptonCornwall / Houghton, MImale
40740710Fox, Mr Stanley H.38SouthamptonRochester, NY229236 L13(236)male
40840810Frost, Mr Anthony (Archie) W.NABelfastmale
40940910Funk, Miss Annie C.38SouthamptonJanjgir, India / Pennsylvaniafemale
41041010Fynney, Mr Joseph J.35SouthamptonLiverpool / Montreal, PQ(322)male
41141110Gale, Mr Harry35SouthamptonCornwall / Clear Creek, COmale
41241210Gale, Mr Shadrach38SouthamptonCornwall / Clear Creek, COmale
41341311Garside, Miss Ethel24SouthamptonBrooklyn, NYfemale
41441410Gaskell, Mr Alfred16SouthamptonLiverpool / Montreal, PQmale
41541510Gavey, Mr Lawrence26SouthamptonGuernsey / Elizabeth, NJmale
41641610Gilbert, Mr William45SouthamptonCornwallmale
41741710Giles, Mr Edgar24SouthamptonCornwall / Camden, NJmale
41841810Giles, Mr Frederick21SouthamptonCornwall / Camden, NJmale
41941910Giles, Mr Ralph22SouthamptonWest Kensington, London(297)male
42042010Gill, Mr John W.NASouthamptonClevedon, Englandmale
42142110Gillespie, Mr William34SouthamptonVancouver, BCmale
42242210Givard, Mr Hans Christensen30Southampton(305)male
42342310Greenberg, Mr Samuel50SouthamptonBronx, NY(19)male
42442410Hale, Mr Reginald30SouthamptonAuburn, NY(75)male
42542511Hamalainen, Mrs William (Anna)23SouthamptonDetroit, MIfemale
42642611Hamalainen, Master Viljo1SouthamptonDetroit, MImale
42742710Harbeck, Mr William H.44SouthamptonSeattle, WA / Toledo, OH248749 L13(35)male
42842810Harper, Rev John28SouthamptonDenmark Hill, Surrey / Chicagomale
42942911Harper, Miss Nina6SouthamptonDenmark Hill, Surrey / Chicago11female
43043011Harris, Mr George30SouthamptonLondonmale
43143110Harris, Mr WalterNASouthamptonWalthamstow, Englandmale
43243210Hart, Mr Benjamin43SouthamptonIlford, Essex / Winnipeg, MB13529 L26 5smale
43343311Hart, Mrs Benjamin (Esther)45SouthamptonIlford, Essex / Winnipeg, MB13529 L26 5s14female
43443411Hart, Miss Eva Miriam7SouthamptonIlford, Essex / Winnipeg, MB13529 L26 5s14female
43543511Herman, Miss Alice24SouthamptonSomerset / Bernardsville, NJ9female
43643611Herman, Miss Kate24SouthamptonSomerset / Bernardsville, NJ9female
43743710Herman, Mr Samuel49SouthamptonSomerset / Bernardsville, NJmale
43843811Herman, Mrs Samuel (Jane Laver)48SouthamptonSomerset / Bernardsville, NJ9female
43943911Hewlett, Mrs Mary D.NASouthamptonIndia / Rapid City, SD13female
44044010Hickman, Mr Leonard Mark34SouthamptonWest Hampstead, London / Neepawa, MB(256)male
44144110Hickman, Mr Lewis32SouthamptonWest Hampstead, London / Neepawa, MBmale
44244210Hickman, Mr Stanley George21SouthamptonWest Hampstead, London / Neepawa, MBmale
44344310Hiltunen, Miss Marta18SouthamptonKontiolahti, Finland / Detroit, MIfemale
44444411Hocking, Mrs Elizabeth53SouthamptonCornwall / Akron, OH4female
44544510Hocking, Mr George23SouthamptonCornwall / Akron, OHmale
44644611Hocking, Miss Ellen (Nellie)21SouthamptonCornwall / Akron, OH4female
44744710Hocking, Mr Samuel JamesNASouthamptonDevonport, Englandmale
44844810Hodges, Mr Henry Price52SouthamptonSouthampton(149)male
44944910Hold, Mr Stephen42SouthamptonEngland / Sacramento, CAmale
45045011Hold, Mrs Stephen (Annie Margaret)36SouthamptonEngland / Sacramento, CAfemale
45145110Hood, Mr Ambrose, Jr21SouthamptonNew Forest, Englandmale
45245211Hosono, Mr Masafumi41SouthamptonTokyo, Japan13male
45345310Howard, Mr BenjaminNASouthamptonSwindon, Englandmale
45445410Howard, Mrs Benjamin (Ellen Truelove)NASouthamptonSwindon, Englandfemale
45545510Hunt, Mr George Henry33SouthamptonPhiladelphia, PAmale
45645611Ilett, Miss Bertha17SouthamptonGuernseyfemale
45745710Jacobsohn Mr Sidney SamuelNASouthamptonLondonmale
45845811Jacobsohn, Mrs Sidney Samuel (Amy Frances Christy)NASouthamptonLondonfemale
45945910Jarvis, Mr John DenzilNASouthamptonNorth Evington, Englandmale
46046010Jefferys, Mr CliffordNASouthamptonGuernsey / Elizabeth, NJmale
46146110Jefferys, Mr ErnestNASouthamptonGuernsey / Elizabeth, NJmale
46246210Jenkin, Mr Stephen CurnowNASouthamptonSt Ives, Cornwall / Houghton, MImale
46346311Jerwan, Mrs Amin S. (Marie Thuillard)23CherbourgNew York, NYfemale
46446410Kantor, Mr Sinai34SouthamptonMoscow / Bronx, NY(283)male
46546511Kantor, Mrs Sinai (Miriam Sternim)NASouthamptonMoscow / Bronx, NYfemale
46646610Karnes, Mrs J. Frank (Claire Bennett)22SouthamptonIndia / Pittsburgh, PAfemale
46746710Keane, Mr DanielNAQueenstownmale
46846811Keane, Miss Nora A.NAQueenstownHarrisburg, PAE-10110female
46946911Kelly, Mrs Florence (Fannie)45SouthamptonLondon / New York, NYfemale
47047010Kirkland, Rev Charles LeonardNAQueenstownGlasgow / Bangor, MEmale
47147110Knight, Mr RobertNABelfastmale
47247210Kvillner, Mr Johan Henrik Johannesson31SouthamptonSweden / Arlington, NJ(165)male
47347310Lahtinen, Rev William30SouthamptonMinneapolis, MNmale
47447410Lahtinen, Mrs William (Anna Sylvan)26SouthamptonMinneapolis, MNfemale
47547510Lamb, Mr John JamesNAQueenstownmale
47647611Lemore, Mrs Amelia34SouthamptonChicago, ILF-3314/Dfemale
47747710LaRoche, Mr Joseph26CherbourgParis / Haitimale
47847811LaRoche, Mrs Joseph (Juliet)22CherbourgParis / Haitifemale
47947911LaRoche, Miss Louise1CherbourgParis / Haitifemale
48048011LaRoche, Miss Simonne3CherbourgParis / Haitifemale
48148111Lehmann, Miss BerthaNACherbourgBerne, Switzerland / Central City, IAfemale
48248211Leitch, Miss JessieNASouthamptonLondon / Chicago, IL11female
48348310Levy, Mr Rene JacquesNACherbourgMontreal, PQmale
48448410Leyson, Mr Robert William Norman25Southampton(108)male
48548510Lingan, Mr JohnNAQueenstownmale
48648610Louch, Mr Charles Alexander48SouthamptonWeston-Super-Mare, Somerset(121)male
48748711Louch, Mrs Charles Alexander (Alice Adelaide)NASouthamptonWeston-Super-Mare, Somerset14female
48848810Mack, Mrs Mary57SouthamptonSouthampton / New York, NYE77(52)female
48948910Malachard, Mr NoelNACherbourgParismale
49049010Mallet, Mr AlbertNACherbourgParis / Montreal, PQmale
49149111Mallet, Mrs Albert (Antoinette)NACherbourgParis / Montreal, PQfemale
49249211Mallet, Master Andre2CherbourgParis / Montreal, PQmale
49349310Mangiavacchi, Mr Serafino EmilioNACherbourgNew York, NYmale
49449410Mantvila, Rev Joseph27SouthamptonWorcester, MAmale
49549511Marshall, Mrs Kate Louise Phillips19SouthamptonWorcester, Englandfemale
49649610Matthews, Mr William John30SouthamptonSt Austall, Cornwallmale
49749710Maybery, Mr Frank H.20SouthamptonWeston-Super-Mare / Moose Jaw, SKmale
49849810McCrae, Mr Arthur Gordon45SouthamptonSydney, Australia(209)male
49949910McCrie, Mr James MatthewNASouthamptonSarnia, ONmale
50050010McKane, Mr Peter D.46SouthamptonRochester, NYmale
50150111Mellenger, Mrs Elizabeth Anne41SouthamptonEngland / Bennington, VT14/12female
50250211Mellenger, Miss Madeleine Violet13SouthamptonEngland / Bennington, VT14/12female
50350311Mellor, Mr William John19SouthamptonChelsea, LondonBmale
50450410Meyer, Mr August30SouthamptonHarrow-on-the-Hill, Middlesexmale
50550510Milling, Mr Jacob Christian48SouthamptonCopenhagen, Denmark(271)male
50650610Mitchell, Mr Henry Michael71SouthamptonGuernsey / Montclair, NJ and/or Toledo, Ohiomale
50750710Moraweck, Dr Ernest54SouthamptonFrankfort, KYmale
50850810Morley, Mr WilliamNASouthamptonPetworth, Sussexmale
50950910Mudd, Mr Thomas C.NASouthamptonHalesworth, Englandmale
51051010Myles, Mr Thomas Francis64QueenstownCambridge, MAmale
51151110Nasser (Nasrallah), Mr Nicholas32CherbourgNew York, NY(43)male
51251211Nasser (Nasrallah), Mrs Nicholas18CherbourgNew York, NYfemale
51351311Navratil, Master Edmond Roger2SouthamptonNice, France230080 L26Dmale
51451410Navratil, Mr Michel32SouthamptonNice, France230080 L26(15)male
51551511Navratil, Master Michel M.3SouthamptonNice, France230080 L26Dmale
51651610Nesson, Mr Israel26SouthamptonBoston, MAmale
51751710Nicholls, Mr Joseph Charles19SouthamptonCornwall / Hancock, MI(101)male
51851810Norman, Mr Robert DouglasNASouthamptonGlasgow(287)male
51951911Nourney, Mr Alfred (aka Baron von Drachstedt)20CherbourgCologne, GermanyD-387male
52052011Nye, Mrs Elizabeth Ramell29SouthamptonFolkstone, Kent / New York, NYF-3311female
52152110Otter, Mr Richard39SouthamptonMiddleburg Heights, OHmale
52252211Oxenham, Mr Percy Thomas22SouthamptonPondersend, England / New Durham, NJmale
52352311Padro y Manent, Mr JulianNACherbourgSpain / Havana, Cubamale
52452410Pain, Dr Alfred24SouthamptonHamilton, ONmale
52552511Pallas y Castello, Mr EmilioNACherbourgSpain / Havana, Cubamale
52652610Parker, Mr Clifford R.28SouthamptonSt Andrews, Guernseymale
52752710Parkes, Mr Francis (Frank)NABelfastmale
52852811Parrish, Mrs Lutie Davis50SouthamptonWoodford County, KY12female
52952910Pengelly, Mr Frederick20SouthamptonGunnislake, England / Butte, MTmale
53053010Peruschitz, Rev. Joseph M.40Southamptonmale
53153111Phillips, Miss Alice42SouthamptonIlfracombe, Devon12female
53253210Phillips, Mr Robert21SouthamptonIlfracombe, Devonmale
53353311Pinsky, Miss Rosa32SouthamptonRussiafemale
53453410Ponesell, Mr Martin34SouthamptonDenmark / New York, NY250647male
53553511Portaluppi, Mr EmilioNACherbourgMilford, NHmale
53653610Pulbaum, Mr FrankNACherbourgParismale
53753711Quick, Mrs Frederick C. (Jane Richards)33SouthamptonPlymouth, Devon / Detroit, MI11female
53853811Quick, Miss Phyllis May2SouthamptonPlymouth, Devon / Detroit, MI11female
53953911Quick, Miss Winifred Vera8SouthamptonPlymouth, Devon / Detroit, MI11female
54054010Reeves, Mr David36SouthamptonBrighton, Sussexmale
54154110Renouf, Mr Peter Henry34SouthamptonElizabeth, NJmale
54254211Renouf, Mrs Peter Henry (Lillian Jefferys)30SouthamptonElizabeth, NJfemale
54354311Reynaldo, Mrs Encarnacion28SouthamptonSpainfemale
54454410Richard, Mr Emil23CherbourgParis / Montreal, PQmale
54554511Richards, Master George Sidney0.8333SouthamptonCornwall / Akron, OH4male
54654611Richards, Mrs Sidney (Emily Hocking)25SouthamptonCornwall / Akron, OH4female
54754711Richards, Master William Rowe3SouthamptonCornwall / Akron, OH4male
54854811Ridsdale, Miss Lucy50SouthamptonLondon, England / Marietta, Ohio and Milwaukee, WIfemale
54954910Rogers, Mr HarryNASouthamptonmale
55055011Rugg, Miss Emily21SouthamptonGuernsey / Wilmington, DE12female
55155110Sedgwick, Mr Charles Frederick WaddingtonNASouthamptonLiverpoolmale
55255210Sharp, Mr PercivalNASouthamptonHornsey, Englandmale
55355311Shelley, Mrs William (Imanita)25SouthamptonDeer Lodge, MT12female
55455411Silven, Miss Lyyli18SouthamptonFinland / Minneapolis, MNfemale
55555511Sincock, Miss Maude20SouthamptonCornwall / Hancock, MI11female
55655611Siukonnen, Miss Anna30SouthamptonFinland / Washington, DCfemale
55755710Sjostedt, Mr Ernst Adolf59SouthamptonSault St Marie, ONmale
55855811Slayter, Miss Hilda Mary30QueenstownHalifax, NS13female
55955910Slemen, Mr Richard James35SouthamptonCornwallmale
56056010Smith (Schmidt), Mr Augustus22SouthamptonNewark, NJmale
56156111Smith, Miss MarionNASouthamptonfemale
56256210Sobey, Mr Hayden25SouthamptonCornwall / Houghton, MImale
56356310Stanton, Mr Samuel Ward41CherbourgNew York, NYmale
56456410Stokes, Mr Philip Joseph25SouthamptonCatford, Kent / Detroit, MI(81)male
56556510Sweet, Mr George14SouthamptonSomerset / Bernardsville, NJmale
56656611Toomey, Miss Ellen50SouthamptonIndianapolis, IN9female
56756710Troupiansky, Mr Moses Aaron22Southamptonmale
56856811Trout, Mrs William H. (Jessie L.)NASouthamptonColumbus, OH9female
56956911Troutt, Miss Edwina Celia27SouthamptonBath, England / MassachusettsE-10134218 L10 10s16female
57057010Turpin, Mr William John29SouthamptonPlymouth, Englandmale
57157110Turpin, Mrs William John (Dorothy Anne Wonnacott)27SouthamptonPlymouth, Englandfemale
57257210Veale, Mr James30SouthamptonBarre, Co Washington, VTmale
57357310Waelens, Mr Achille22SouthamptonAntwerp, Belgium / Stanton, OH(140)male
57457411Walcroft, Miss Nellie35SouthamptonMamaroneck, NYfemale
57557510Ware, Mr John James30SouthamptonBristol, England / New Britain, CTmale
57657611Ware, Mrs John James (Florence Louise Long)28SouthamptonBristol, England / New Britain, CT12female
57757710Ware, Mr William J.23Southamptonmale
57857810Watson, Mr Ennis HastingsNASouthamptonBelfastmale
57957911Watt, Miss Bertha12SouthamptonAberdeen / Portland, OR9female
58058011Watt, Mrs James (Bessie Inglis Milne)40SouthamptonAberdeen / Portland, OR9female
58158111Webber, Miss Susan36SouthamptonEngland / Hartford, CTE-101female
58258210Weisz, Mr Leopold28SouthamptonBromsgrove, England / Montreal, PQ(293)male
58358311Weisz, Mrs Leopold (Mathilde)32SouthamptonBromsgrove, England / Montreal, PQfemale
58458411Wells, Mrs Arthur H. (Addie Trevaskis)29SouthamptonCornwall / Akron, OHfemale
58558511Wells, Miss Joan4SouthamptonCornwall / Akron, OHfemale
58658611Wells, Master Ralph Lester2SouthamptonCornwall / Akron, OHmale
58758711West, Miss Barbara J.NASouthamptonBournmouth, Englandfemale
58858811West, Miss Constance MiriumNASouthamptonBournmouth, Englandfemale
58958910West, Mr Edwy Arthur36SouthamptonBournmouth, Englandmale
59059011West, Mrs Edwy Arthur (Ada Mary)33SouthamptonBournmouth, Englandfemale
59159110Wheadon, Mr EdwardNASouthamptonGuernsey, England / Edgewood, RImale
59259210Wheeler, Mr EdwinNASouthamptonmale
59359310Wheeler, Mr FrederickNAmale
59459411Wilhelms, Mr Charles32SouthamptonLondon, England9male
59559511Wilkinson, Mrs Elizabeth AnneNASouthamptonManchester, Englandfemale
59659611Williams, Mr Charles EugeneNASouthamptonHarrow, England14male
59759711Wright, Miss Marion26SouthamptonYoevil, England / Cottage Grove, OR9female
59859810Yrois, Miss HenrietteNASouthamptonParisfemale
59959910Aldworth, Mr Charles Augustus30SouthamptonBryn Mawr, PA, USA248744 L13male
60060011Brown, Miss Mildred24SouthamptonLondon / Montreal, PQF-3311female
60160110Pernot, Mr ReneNACherbourg2131L15 1smale
60260210Swane, Mr George18SouthamptonF-?(294)male
60360300Abbing, Mr Anthony42Southamptonmale
60460400Abbott, Master Eugene Joseph13SouthamptonEast Providence, RImale
60560500Abbott, Mr Rossmore Edward16SouthamptonEast Providence, RI(190)male
60660601Abbott, Mrs Stanton (Rosa)35SouthamptonEast Providence, RIAfemale
60760701Abelseth, Miss Anna Karen16SouthamptonNorway Los Angeles, CA16female
60860801Abelseth, Mr Olaus25SouthamptonPerkins County, SDAmale
60960901Abraham, Mrs Joseph (Sophie Easu)18CherbourgGreensburg, PAfemale
61061001Abrahamsson, Mr August20SouthamptonTaalintehdas, Finland Hoboken, NJ15male
61161100Adahl, Mr Mauritz Nils Martin30SouthamptonAsarum, Sweden Brooklyn, NY7076(72)male
61261200Adams, Mr John26SouthamptonBournemouth, England(103)male
61361300Ahlin, Mrs Johanna Persdotter40SouthamptonSweden Akeley, MNfemale
61461400Ahmed, Mr Ali24Southamptonmale
61561500Aijo-Nirva, Mr Isak41SouthamptonFinland Sudbury, ONmale
61661601Aks, Mrs Sam (Leah Rosen)18SouthamptonLondon, England Norfolk, VA39209113female
61761701Aks, Master Philip0.8333SouthamptonLondon, England Norfolk, VA39209111male
61861800Alexander, Mr William23SouthamptonEngland Albion, NYmale
61961900Alhomaki, Mr Ilmari Rudolf20SouthamptonSalo, Finland Astoria, ORmale
62062000Ali, Mr William25SouthamptonArgentina(79)male
62162100Allen, Mr William Henry35SouthamptonLower Clapton, Middlesex or Erdington, Birminghammale
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62362300Andersen, Mr Albert Karvin32SouthamptonBergen, Norway(260)male
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62562500Andersson, Mr Anders Johan39SouthamptonSweden Winnipeg, MNmale
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63063000Andersson, Miss Ida Augusta Margareta38SouthamptonVadsbro, Sweden Ministee, MIfemale
63163100Andersson, Miss Ingeborg Constancia9SouthamptonSweden Winnipeg, MNfemale
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63563500Andreasson, Mr Paul Edvin20SouthamptonSweden Chicago, ILmale
63663600Angheloff, Mr Minko26SouthamptonBulgaria Chicago, ILmale
63763700Arnold, Mr Josef25SouthamptonAltdorf, Switzerlandmale
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63963900Aronsson, Mr Ernst Axel Algot24SouthamptonSweden Joliet, ILmale
64064000Asim, Mr Adola35Southamptonmale
64164100Asplund, Mr Carl Oscar Vilhelm Gustafsson40SouthamptonSweden Worcester, MA(142)male
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64364300Asplund, Master Carl Edgar5SouthamptonSweden Worcester, MAmale
64464400Asplund, Master Clarence Gustaf Hugo9SouthamptonSweden Worcester, MAmale
64564501Aspland, Master Edvin Rojj Felix3SouthamptonSweden Worcester, MA4male
64664600Asplund, Master Filip Oscar13SouthamptonSweden Worcester, MAmale
64764701Asplund, Mr John Charles23SouthamptonOskarshamn, Sweden Minneapolis, MNmale
64864801Asplund, Miss Lillian Gertrud5SouthamptonSweden Worcester, MA4female
64964900Assaf, Mr GeriosNACherbourgOttawa, ONmale
65065001Assaf, Mrs Mariana45CherbourgOttawa, ONCfemale
65165100Assam, Mr Ali23Southamptonmale
65265200Attalah, Miss Malaka17Cherbourgfemale
65365300Attala (Kalil), Mr Solomon27CherbourgOttawa, ONmale
65465400Augustsson, Mr Albert23SouthamptonKrakoryd, Sweden Bloomington, ILmale
65565500Baccos, Mr Rafoul20Cherbourgmale
65665600Backstrom, Mr Karl Alfred32SouthamptonRuotsinphytaa, Finland New York, NYmale
65765701Backstrom, Mrs Karl Alfred (Maria Mathilda Gustafsson)33SouthamptonRuotsinphytaa, Finland New York, NYfemale
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66166101Baclini, Mrs Solomon (Latifa)NACherbourgSyria New York, NYfemale
66266201Badman, Miss Emily Louisa18SouthamptonLondon Skanteales, NYfemale
66366300Badt, Mr Mohamed40Cherbourgmale
66466400Balkic, Mr Cerin26Southamptonmale
66566501Banoura, Miss Ayout15CherbourgSyria Youngstown, OHfemale
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67067000Beavan, Mr William Thomas19SouthamptonEnglandmale
67167100Bengtsson, Mr John Viktor26SouthamptonKrakudden, Sweden Moune, ILmale
67267200Berglund. Mr Karl Ivar Sven22SouthamptonTranvik, Finland New Yorkmale
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67467401Bing, Mr Lee32SouthamptonHong Kong New York, NYmale
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67667600Bjorklund, Ernst Herbert18SouthamptonStockholm, Sweden New Yorkmale
67767700Bostandyeff, Mr Guentcho26SouthamptonBulgaria Chicago, ILmale
67867800Boulos, Master Akar6CherbourgSyria Kent, ONmale
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69069000Braund, Mr Owen Harris22SouthamptonBridgerule, Devonmale
69169100Brobek, Mr Karl Rudolf22SouthamptonSweden Worcester, MAmale
69269200Brocklebank, Mr William Alfred35SouthamptonBroomfield, Chelmsford, Englandmale
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69669600Burns, Miss Mary Delia18QueenstownCo Sligo, Ireland New York, NYfemale
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74074000Coxon, Mr Daniel59SouthamptonMerrill, WImale
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75875800Davies, Mr Joseph17SouthamptonWest Bromwich, England Pontiac, MImale
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76676601De Messemaeker, Mr William Joseph36SouthamptonTampico, MT15male
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1053105300Nancarrow, W. H.NAmale
1054105400Niklasen, SanderNAmale
1055105500Nosworthy, Richard C.NAmale
1056105601Najib, Miss Adele KiamieNAfemale
1057105700Nancarrow, Mr William HenryNAmale
1058105800Nankoff, Mr MinkoNAmale
1059105900Nasr, Mr MustafaNAmale
1060106000Nassr, Mr Saade JeanNAmale
1061106100Naughton, Miss HannahNAfemale
1062106200Nemaugh, Mr RobertNAmale
1063106300Nenkoff, Mr ChristoNAmale
1064106401Nicola-Yarred, Miss JamilaNAfemale
1065106500Nicola-Yarred, Master EliasNAmale
1066106600Nieminen, Miss Manta JosefinaNAfemale
1067106700Niklasson, Mr SamuelNAmale
1068106800Nilsson, Mr August FerdinandNAmale
1069106901Nilsson, Miss Berta OliviaNAfemale
1070107000Nilsson, Miss Helmina JosefinaNAfemale
1071107100Niskanen, Mr JohanNAmale
1072107200Nosworthy, Mr Richard CaterNAmale
1073107301Novel, MansouerNAmale
1074107400Nysten, Miss AnnaNAfemale
1075107500Nysveen, Mr Johan H.NAmale
1076107600O'Brien, Mr DenisNAmale
1077107700O'Brien, Mr ThomasNAmale
1078107801O'Brien, Mrs ThomasNAfemale
1079107900O'Connell, Mr Patrick D.NAmale
1080108000O'Connor, Mr MauriceNAmale
1081108100O'Connor, Mr PatrickNAmale
1082108201Odahl, Mr Nils MartinNAmale
1083108300O'Dwyer, Miss NellieNAfemale
1084108400Ohman, Miss VelinNAfemale
1085108500O'Keefe, Mr PatrickNAmale
1086108600OLeary, Miss NorahNAfemale
1087108700Olsen, Master ArthurNAmale
1088108800Olsen, Mr Charlie (Carl)NAmale
1089108900Olsen, Mr Henry MargidoNAmale
1090109000Olsen, Mr Ole M.NAmale
1091109100Olsson, Miss ElidaNAfemale
1092109200Olsson, Mr Nils JohanNAmale
1093109301Olsson, Mr Oscar JohanssonNAmale
1094109400O'Neill, Miss BridgetNAfemale
1095109500Oreskovic, Mr JekoNAmale
1096109600Oreskovic, Mr LukaNAmale
1097109700Oreskovic, Mr MariaNAmale
1098109800Osen, Mr Olof ElonNAmale
1099109901Osman, Miss MariaNAfemale
1100110000O'Sullivan, Miss BridgetNAfemale
1101110100Panula, Mr Ernesti ArvidNAmale
1102110200Panula, Mr Jaako ArnoldNAmale
1103110300Panula, Master Juha NiiloNAmale
1104110400Panula, Mrs JohnNAfemale
1105110500Panula, Master Urho AbrahamNAmale
1106110600Panula, Master WilliamNAmale
1107110700Pasic, Mr JakobNAmale
1108110800Paulner, Mr UscherNAmale
1109110900Paulsson, Master Gosta LeonardNAmale
1110111000Paulsson, Mrs NilsNAfemale
1111111100Paulsson, Master Paul FolkeNAmale
1112111200Paulsson, Miss Stina ViolaNAfemale
1113111300Paulsson, Miss Torborg DaniraNAfemale
1114111400Pavlovic, Mr StefoNAmale
1115111500Peacock, Master Alfred EdwardNAmale
1116111600Peacock, Mrs BenjaminNAfemale
1117111700Peacock, Miss TreasteallNAfemale
1118111800Pearce, Mr ErnestNAmale
1119111900Pecruic, Mr MateNAmale
1120112000Pecruic, Mr TomeNAmale
1121112100Pedersen, Mr OlafNAmale
1122112200Peduzzi, Mr JosephNAmale
1123112301Pekoniemi, Mr EdvardNAmale
1124112400Peltomaki, Nikolai JohannesNAmale
1125112500Perkin, Mr John HenryNAmale
1126112601Persson, Mr Ernst UlrikNAmale
1127112700Peter (Joseph), Miss MaryNAfemale
1128112800Peter (Joseph), Mrs CatherineNAfemale
1129112900Peter (Joseph), Master Michael J.NAmale
1130113000Peters, Miss KatieNAfemale
1131113100Petersen, Mr MariusNAmale
1132113200Petranec, Miss MatildaNAfemale
1133113300Petroff, Mr NedecaNAmale
1134113400Petroff, Mr PentchoNAmale
1135113500Pettersson, Miss Ellen NataliaNAfemale
1136113600Peterson, Mr Johan EmilNAmale
1137113701Pickard (Trembisky), Mr BerkNAmale
1138113800Plotharsky, Mr VasilNAmale
1139113900Potchett, Mr GeorgeNAmale
1140114000Radeff, Mr AlexanderNAmale
1141114100Raibid, Mr RaziNAmale
1142114200Reed, Mr James GeorgeNAmale
1143114300Reynolds, Mr HaroldNAmale
1144114400Rice, Master AlbertNAmale
1145114500Rice, Master ArthurNAmale
1146114600Rice, Master GeorgeNAmale
1147114700Rice, Master EricNAmale
1148114800Rice, Master EugeneNAmale
1149114900Rice, Mrs WilliamNAfemale
1150115000Riihiivouri, Miss SanniNAfemale
1151115100Rintamaki, Mr MattiNAmale
1152115201Riordan, Miss HannahNAfemale
1153115300Risien, Mr SamuelNAmale
1154115400Risien, Mrs SamuelNAfemale
1155115500Robins, Mr Alexander A.NAmale
1156115600Robins, Mrs Alexander A.NAfemale
1157115700Rommetvedt, Mr Karl Kristian KnutNAmale
1158115800Rogers, Mr William JohnNAmale
1159115900Rosblom, Mrs ViktorNAfemale
1160116000Rosblom, Miss Salli HelenaNAfemale
1161116100Rosblom, Mr Viktor RickardNAmale
1162116201Roth, Miss SarahNAfemale
1163116300Rouse, Mr Richard HenryNAmale
1164116400Rush, Mr Alfred George JohnNAmale
1165116501Ryan, Mr Edward RyanNAmale
1166116600Ryan, Mr PatrickNAmale
1167116700Saad, Mr AminNAmale
1168116801Saad, KhalilNAmale
1169116900Sadlier, Mr MatthewNAmale
1170117000Sadowitz, Mr HarryNAmale
1171117100Sage, Miss AdaNAfemale
1172117200Sage, Miss ConstanceNAfemale
1173117300Sage, Miss DorothyNAfemale
1174117400Sage, Mr DouglasNAmale
1175117500Sage, Mr FrederickNAmale
1176117600Sage, Mr GeorgeNAmale
1177117700Sage, Mr JohnNAmale
1178117800Sage, Mrs JohnNAfemale
1179117900Sage, Miss StellaNAfemale
1180118000Sage, Thomas (child)NAmale
1181118100Sage, Master WilliamNAmale
1182118200Salander, Mr Karl JohanNAmale
1183118301Salkjelsvik, Miss AnnaNAfemale
1184118400Salonen, Mr Johan WernerNAmale
1185118500Samaan, Mr EliasNAmale
1186118600Samaan, Mr HannaNAmale
1187118700Samaan, Mr YoussefNAmale
1188118801Sandstrom, Miss HjalmarNAfemale
1189118900Sandstrom, Miss Beatrice IreneNAfemale
1190119000Sandstrom, Miss Marguerite RutNAfemale
1191119100Sather, Simon SivertsenNAmale
1192119200Saundercock, William HenryNAmale
1193119300Sawyer, Mr FrederickNAmale
1194119400Scanlan, Mr JamesNAmale
1195119500Sdycoff, Mr TodorNAmale
1196119600Seman Master BetrosNAmale
1197119700Serota, Mr MauriceNAmale
1198119800Shaughnesay, Mr PatrickNAmale
1199119900Shedid (Sitik), Mr Daher (Docart)NAmale
1200120001Sheerlinck, Mr JeanNAmale
1201120100Shellard, Mr Frederick B.NAmale
1202120201Shine, Miss EllenNAfemale
1203120300Shorney, Mr CharlesNAmale
1204120400Simmons, Mr JohnNAmale
1205120500Sirayanian, Mr ArsunNAmale
1206120600Sivic, Mr HusenNAmale
1207120700Sivola, Mr AnttiNAmale
1208120801Sjoblom, Miss Anna SofiaNAfemale
1209120900Sholt, Mr Peter Andreas Lauritz AndersenNAmale
1210121000Skinner, Mr Henry JohnNAmale
1211121100Skoog, Master HaraldNAmale
1212121200Skoog, Master KarlNAmale
1213121300Skoog, Miss MabelNAfemale
1214121400Skoog, Miss MargitNAfemale
1215121500Skoog, Mr WilliamNAmale
1216121600Skoog, Mrs WilliamNAfemale
1217121700Slabenoff, Mr PetcoNAmale
1218121800Slocovski, Mr SelmanNAmale
1219121900Smiljanovic, Mr MileNAmale
1220122001Smyth, Miss JuliaNAfemale
1221122100Solvang, Mrs Lena JacobsenNAfemale
1222122200Somerton, Mr Francis WilliamNAmale
1223122301Sop, Mr JulesNAmale
1224122400Spector, Mr WoolfNAmale
1225122500Staneff, Mr IvanNAmale
1226122600Stankovic, Mr JovanNAmale
1227122701Stanley, Miss Amy Zilla ElsieNAfemale
1228122800Stanley, Mr Edward RolandNAmale
1229122900Storey, Mr ThomasNAmale
1230123000Stoyehoff, Mr IliaNAmale
1231123100Strandberg, Miss Ida SofiaNAfemale
1232123201Stranden, Mr JuhoNAmale
1233123300Strilic, Mr IvanNAmale
1234123400Strom, Mrs WilhelmNAfemale
1235123500Strom, Miss Telma (Selma) MatildaNAfemale
1236123601Sunderland, Mr Victor FrancisNAmale
1237123700Sundman, Mr Johan JulianNAmale
1238123800Sutehall, Mr Henry, JrNAmale
1239123900Svensson, Mr JohanNAmale
1240124001Svensson, Mr Johan CervinNAmale
1241124100Svensson, Mr OlofNAmale
1242124200Tannous, Mr ThomasNAmale
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1244124400Theobald, Mr Thomas LeonardNAmale
1245124501Thomas, Mrs AlexanderNAfemale
1246124600Thomas, Master Assad AlexanderNAmale
1247124700Thomas, Mr CharlesNAmale
1248124800Thomas, Mr John, JrNAmale
1249124900Thomas, Mr John (? 1st/2nd class)NAmale
1250125000Thomson, Mr AlexanderNAmale
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1255125500Todoroff, Mr LalioNAmale
1256125600Toerber, Mr Ernest WilliamNAmale
1257125700Tomlin, Mr Ernest PortageNAmale
1258125800Torfa, Mr AssadNAmale
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1260126000Touma (Thomas), Mrs DarwinNAfemale
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1272127200Van der Planke, Mrs JulesNAfemale
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1311131100Zenn, Mr PhilipNAmale
1312131200Zievens, ReneNAfemale
1313131300Zimmerman, LeoNAmale
fit.survive<-glm(survived ~ sex + age +pclass,family= "binomial")
summary(fit.survive)
Call:
glm(formula = survived ~ sex + age + pclass, family = "binomial")

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-2.9784  -0.6520  -0.3142   0.5894   2.7022

Coefficients:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)  4.522163   0.471008   9.601  < 2e-16 *
sexmale     -3.086709   0.241063 -12.805  < 2e-16 *
age         -0.049309   0.008732  -5.647 1.63e-08 *
pclass2nd   -1.495229   0.281986  -5.302 1.14e-07 *
pclass3rd   -2.841271   0.338897  -8.384  < 2e-16 *
---
Signif. codes:  0 ‘*’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 869.54  on 632  degrees of freedom
Residual deviance: 539.71  on 628  degrees of freedom
  (680 observations deleted due to missingness)
AIC: 549.71

Number of Fisher Scoring iterations: 5
fit.survive<-glm(survived ~ sex + age + pclass + sex:pclass + age:pclass,family= "binomial")
summary(fit.survive)
Call:
glm(formula = survived ~ sex + age + pclass + sex:pclass + age:pclass,
    family = "binomial")

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-3.0532  -0.6111  -0.3829   0.4168   2.5174

Coefficients:
                   Estimate Std. Error z value Pr(>|z|)
(Intercept)        4.736466   0.756171   6.264 3.76e-10 *
sexmale           -3.685635   0.510927  -7.214 5.45e-13 *
age               -0.042485   0.013044  -3.257  0.00113 **
pclass2nd          0.232062   1.095137   0.212  0.83218
pclass3rd         -3.978596   0.888172  -4.480 7.48e-06 *
sexmale:pclass2nd -0.655681   0.735503  -0.891  0.37268
sexmale:pclass3rd  1.870332   0.631770   2.960  0.00307 **
age:pclass2nd     -0.049047   0.023427  -2.094  0.03629 *
age:pclass3rd      0.007216   0.021396   0.337  0.73593
---
Signif. codes:  0 ‘*’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 869.54  on 632  degrees of freedom
Residual deviance: 517.73  on 624  degrees of freedom
  (680 observations deleted due to missingness)
AIC: 535.73

Number of Fisher Scoring iterations: 5
detach(Titanic)

Negative Binomial

When \(Y\) follows a negative binomial distribution, we model the mean as:

\[\mathbb{E}(Y|x) = exp(\alpha + \beta x)\]

What is the link function?

The following example is lifted from http://www.ats.ucla.edu/stat/r/dae/nbreg.htm

library(foreign)
library(ggplot2)
library(MASS)
dat <- read.dta("http://www.ats.ucla.edu/stat/stata/dae/nb_data.dta")
dat
idgendermathdaysabsprog
11001male6342
21002male2742
31003female2022
41004female1632
51005female232
61006female71132
71007female63112
81008male372
91009male51102
101010male4993
111011female3143
121012male2252
131013female7352
141014female7761
151015male1013
161016male8902
171017female3412
181018female3502
191019male7751
201020male4242
211021female2122
221022male6102
231023male4112
241024male6302
251025female1982
261026male5561
271027male672
281028female2102
291029male7022
301030male7931
311031male102
321032female2912
331033male4032
341034male3902
351035male6802
361036female20282
371037male1082
381038male8452
391039male151
401040female35272
411041female3252
421042female34182
431043female40192
441044male2992
451045male2092
461046female2742
471047male7422
481048male3832
491049male2192
501050female81202
511051male1662
521052male5902
531053male48272
541054female55122
551055female4342
561056male5712
571057male5281
581058male381
591059female2332
601060female3522
611061male3312
621062female2772
631063male1342
641064male4682
651065female3062
661066male32162
671067female2661
681068female1442
691069female3133
701070female4852
711071male7202
721072male7992
731073male1503
741074male2482
751075female5503
761076female13141
771077male3442
781078male6722
791079male1352
801080female21232
811081female33132
821082male7862
831083female8431
841084male5962
851085male7502
861086male22111
871087female49112
881088female13112
891089male8443
901090male2762
911091female27232
921092female7052
931093male9652
941094female70291
951095female1072
961096male1412
971097male2092
981098male11112
991099male42182
1001100male2122
1011101male2461
1021102male3702
1031103male1342
1041104male3102
1051105male70191
1061106female2712
1071107female1121
1081108female6132
1091109male4402
1101110male3592
1111111male78142
1121112female372
1131113male2132
1141114male26102
1151115male44122
1161116female4762
1171117female35352
1181118female8161
1191119female8732
1201120male3102
1211121male662
1221122male8931
1231123male1322
1241124male8462
1251125male9052
1261126female71132
1271127female1571
1281128female4152
1291129female6332
1301130female34302
1311131female45162
1321132female29152
1331133female3122
1341134male3512
1351135male3241
1361136male2272
1371137female8112
1381139female73102
1391140male6932
1401141female27301
1411142female1322
1421143female76132
1431144female751
1441145male5952
1451146female2952
1461147female5742
1471148female4432
1481149female53202
1491150female23122
1501151female29341
1511152male4062
1521153male49142
1531154female38161
1541155male3191
1551156female21151
1561157male8151
1571158male3702
1581159male5312
1592001female3143
1602002male5703
1612003male5703
1622004male5923
1632005female2913
1642006female4122
1652007male7103
1662008female5903
1672009male7103
1682010female7073
1692011male7723
1702012female7092
1712013female8763
1722014male5943
1732015male6513
1742016female2872
1752017male7703
1762018male6503
1772019female7343
1782020male9922
1792021female5703
1802022female7743
1812023female5722
1822024female47211
1832025female2413
1842026male8403
1852027female7313
1862028male81163
1872029female5291
1882030female75163
1892031male6502
1902032female44111
1912033male4413
1922034female7923
1932035female2033
1942036female1642
1952037female9922
1962038female7171
1972039male4673
1982040female5702
1992041female6712
2002042female8713
2012043female7003
2022044female21133
2032045female3113
2042046male6303
2052047female4412
2062048male3403
2072049female7741
2082050female9403
2092051female4141
2102052female6703
2112053female6123
2122054male8203
2132055female6341
2142056male6303
2152057female7743
2162058male4633
2172059male813
2182060female6102
2192061female7112
2202062female6543
2212063female4112
2222064male1692
2232065female2203
2242066male5742
2252067female5182
2262068male74132
2272069male4103
2282070male8703
2292071male6703
2302072female9902
2312073female6322
2322074female6553
2332075female7113
2342076male7703
2352077female6731
2362078female7912
2372079female2023
2382080male8441
2392081male2852
2402082female2033
2412083male2613
2422084female7532
2432085female6363
2442086male3983
2452087male32212
2462088male1512
2472089female5573
2482090female3252
2492091male3412
2502092female6713
2512093female4103
2522094male4143
2532095female2902
2542096male43143
2552097female7722
2562098female5323
2572099female4423
2582100male5103
2592101male6713
2602102male49193
2612103female3722
2622104male65113
2632105male4331
2642106female4852
2652107female99161
2662108female3403
2672109male8753
2682110male7533
2692111female5722
2702112male6123
2712113male7381
2722114female7003
2732115female9933
2742116male7303
2752117male6613
2762118male5792
2772119male7713
2782120male5303
2792121male7303
2802122male8413
2812123male83122
2822124female7733
2832125male4403
2842126female7913
2852127male5381
2862128female4313
2872129male4613
2882130female3572
2892131female6363
2902132female7503
2912133female8483
2922134male4102
2932135female3213
2942136male1202
2952137male6143
2962138female99172
2972139male6791
2982140female3503
2992141female7003
3002142female8713
3012143male7033
3022144male5712
3032145male4423
3042146female2623
3052147male6323
3062148female852
3072150male6333
3082151female5973
3092152female4613
3102153male2612
3112154female7933
3122155female5902
3132156female9003
3142157female7723
dat <- within(dat, {
    prog <- factor(prog, levels = 1:3, labels = c("General", "Academic", "Vocational"))
    id <- factor(id)
})

summary(dat)
      id         gender         math          daysabs               prog
1001   :  1   female:160   Min.   : 1.00   Min.   : 0.000   General   : 40
1002   :  1   male  :154   1st Qu.:28.00   1st Qu.: 1.000   Academic  :167
1003   :  1                Median :48.00   Median : 4.000   Vocational:107
1004   :  1                Mean   :48.27   Mean   : 5.955
1005   :  1                3rd Qu.:70.00   3rd Qu.: 8.000
1006   :  1                Max.   :99.00   Max.   :35.000
(Other):308
ggplot(dat, aes(daysabs, fill = prog)) + geom_histogram(binwidth = 1) + facet_grid(prog ~
    ., margins = TRUE, scales = "free")
_images/LogisticRegression_29_0.png
m1 <- glm.nb(daysabs ~ math + prog, data = dat)
summary(m1)
Call:
glm.nb(formula = daysabs ~ math + prog, data = dat, init.theta = 1.032713156,
    link = log)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-2.1547  -1.0192  -0.3694   0.2285   2.5273

Coefficients:
                Estimate Std. Error z value Pr(>|z|)
(Intercept)     2.615265   0.197460  13.245  < 2e-16 *
math           -0.005993   0.002505  -2.392   0.0167 *
progAcademic   -0.440760   0.182610  -2.414   0.0158 *
progVocational -1.278651   0.200720  -6.370 1.89e-10 *
---
Signif. codes:  0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(1.0327) family taken to be 1)

    Null deviance: 427.54  on 313  degrees of freedom
Residual deviance: 358.52  on 310  degrees of freedom
AIC: 1741.3

Number of Fisher Scoring iterations: 1


              Theta:  1.033
          Std. Err.:  0.106

 2 x log-likelihood:  -1731.258